Differentiation formulas pdf

• • • • • Classes • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • n th Order Linear Equations • • • • • • • • • • • • • • • • • • • • • • • • • Extras • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Misc Links • • • • • • You appear to be on a device with a "narrow" screen width ( i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width. Section 3.3 : Differentiation Formulas For problems 1 – 12 find the derivative of the given function. • \(f\left( x \right) = 6 + x\) is parallel to the line \(y = 4x + 23\).

Learning Objectives • 3.3.1 State the constant, constant multiple, and power rules. • 3.3.2 Apply the sum and difference rules to combine derivatives. • 3.3.3 Use the product rule for finding the derivative of a product of functions. • 3.3.4 Use the quotient rule for finding the derivative of a quotient of functions. • 3.3.5 Extend the power rule to functions with negative exponents. • 3.3.6 Combine the differentiation rules to find the derivative of a polynomial or rational function. Finding derivatives of functions by using the definition of the derivative can be a lengthy and, for certain functions, a rather challenging process. For example, previously we found that d d x ( x ) = 1 2 x d d x ( x ) = 1 2 x by using a process that involved multiplying an expression by a conjugate prior to evaluating a limit. The process that we could use to evaluate d d x ( x 3 ) d d x ( x 3 ) using the definition, while similar, is more complicated. In this section, we develop rules for finding derivatives that allow us to bypass this process. We begin with the basics. The Basic Rules The functions f ( x ) = c f ( x ) = c and g ( x ) = x n g ( x ) = x n where n n is a positive integer are the building blocks from which all polynomials and rational functions are constructed. To find derivatives of polynomials and rational functions efficiently without resorting to the limit definition of the derivative, we must first develop formulas for differentiating these basic functions. The Constant...

• • • • • Classes • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • n th Order Linear Equations • • • • • • • • • • • • • • • • • • • • • • • • • Extras • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Misc Links • • • • • • You appear to be on a device with a "narrow" screen width ( i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width. Section 3.3 : Differentiation Formulas For problems 1 – 12 find the derivative of the given function. • \(f\left( x \right) = 6 + x\) is parallel to the line \(y = 4x + 23\).

Learning Objectives • 3.3.1 State the constant, constant multiple, and power rules. • 3.3.2 Apply the sum and difference rules to combine derivatives. • 3.3.3 Use the product rule for finding the derivative of a product of functions. • 3.3.4 Use the quotient rule for finding the derivative of a quotient of functions. • 3.3.5 Extend the power rule to functions with negative exponents. • 3.3.6 Combine the differentiation rules to find the derivative of a polynomial or rational function. Finding derivatives of functions by using the definition of the derivative can be a lengthy and, for certain functions, a rather challenging process. For example, previously we found that d d x ( x ) = 1 2 x d d x ( x ) = 1 2 x by using a process that involved multiplying an expression by a conjugate prior to evaluating a limit. The process that we could use to evaluate d d x ( x 3 ) d d x ( x 3 ) using the definition, while similar, is more complicated. In this section, we develop rules for finding derivatives that allow us to bypass this process. We begin with the basics. The Basic Rules The functions f ( x ) = c f ( x ) = c and g ( x ) = x n g ( x ) = x n where n n is a positive integer are the building blocks from which all polynomials and rational functions are constructed. To find derivatives of polynomials and rational functions efficiently without resorting to the limit definition of the derivative, we must first develop formulas for differentiating these basic functions. The Constant...

Learning Objectives • 3.3.1 State the constant, constant multiple, and power rules. • 3.3.2 Apply the sum and difference rules to combine derivatives. • 3.3.3 Use the product rule for finding the derivative of a product of functions. • 3.3.4 Use the quotient rule for finding the derivative of a quotient of functions. • 3.3.5 Extend the power rule to functions with negative exponents. • 3.3.6 Combine the differentiation rules to find the derivative of a polynomial or rational function. Finding derivatives of functions by using the definition of the derivative can be a lengthy and, for certain functions, a rather challenging process. For example, previously we found that d d x ( x ) = 1 2 x d d x ( x ) = 1 2 x by using a process that involved multiplying an expression by a conjugate prior to evaluating a limit. The process that we could use to evaluate d d x ( x 3 ) d d x ( x 3 ) using the definition, while similar, is more complicated. In this section, we develop rules for finding derivatives that allow us to bypass this process. We begin with the basics. The Basic Rules The functions f ( x ) = c f ( x ) = c and g ( x ) = x n g ( x ) = x n where n n is a positive integer are the building blocks from which all polynomials and rational functions are constructed. To find derivatives of polynomials and rational functions efficiently without resorting to the limit definition of the derivative, we must first develop formulas for differentiating these basic functions. The Constant...

• • • • • Classes • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • n th Order Linear Equations • • • • • • • • • • • • • • • • • • • • • • • • • Extras • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Misc Links • • • • • • You appear to be on a device with a "narrow" screen width ( i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width. Section 3.3 : Differentiation Formulas For problems 1 – 12 find the derivative of the given function. • \(f\left( x \right) = 6 + x\) is parallel to the line \(y = 4x + 23\).

• • • • • Classes • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • n th Order Linear Equations • • • • • • • • • • • • • • • • • • • • • • • • • Extras • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Misc Links • • • • • • You appear to be on a device with a "narrow" screen width ( i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width. Section 3.3 : Differentiation Formulas For problems 1 – 12 find the derivative of the given function. • \(f\left( x \right) = 6 + x\) is parallel to the line \(y = 4x + 23\).

Learning Objectives • 3.3.1 State the constant, constant multiple, and power rules. • 3.3.2 Apply the sum and difference rules to combine derivatives. • 3.3.3 Use the product rule for finding the derivative of a product of functions. • 3.3.4 Use the quotient rule for finding the derivative of a quotient of functions. • 3.3.5 Extend the power rule to functions with negative exponents. • 3.3.6 Combine the differentiation rules to find the derivative of a polynomial or rational function. Finding derivatives of functions by using the definition of the derivative can be a lengthy and, for certain functions, a rather challenging process. For example, previously we found that d d x ( x ) = 1 2 x d d x ( x ) = 1 2 x by using a process that involved multiplying an expression by a conjugate prior to evaluating a limit. The process that we could use to evaluate d d x ( x 3 ) d d x ( x 3 ) using the definition, while similar, is more complicated. In this section, we develop rules for finding derivatives that allow us to bypass this process. We begin with the basics. The Basic Rules The functions f ( x ) = c f ( x ) = c and g ( x ) = x n g ( x ) = x n where n n is a positive integer are the building blocks from which all polynomials and rational functions are constructed. To find derivatives of polynomials and rational functions efficiently without resorting to the limit definition of the derivative, we must first develop formulas for differentiating these basic functions. The Constant...

• • • • • Classes • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • n th Order Linear Equations • • • • • • • • • • • • • • • • • • • • • • • • • Extras • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Misc Links • • • • • • You appear to be on a device with a "narrow" screen width ( i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width. Section 3.3 : Differentiation Formulas For problems 1 – 12 find the derivative of the given function. • \(f\left( x \right) = 6 + x\) is parallel to the line \(y = 4x + 23\).

Learning Objectives • 3.3.1 State the constant, constant multiple, and power rules. • 3.3.2 Apply the sum and difference rules to combine derivatives. • 3.3.3 Use the product rule for finding the derivative of a product of functions. • 3.3.4 Use the quotient rule for finding the derivative of a quotient of functions. • 3.3.5 Extend the power rule to functions with negative exponents. • 3.3.6 Combine the differentiation rules to find the derivative of a polynomial or rational function. Finding derivatives of functions by using the definition of the derivative can be a lengthy and, for certain functions, a rather challenging process. For example, previously we found that d d x ( x ) = 1 2 x d d x ( x ) = 1 2 x by using a process that involved multiplying an expression by a conjugate prior to evaluating a limit. The process that we could use to evaluate d d x ( x 3 ) d d x ( x 3 ) using the definition, while similar, is more complicated. In this section, we develop rules for finding derivatives that allow us to bypass this process. We begin with the basics. The Basic Rules The functions f ( x ) = c f ( x ) = c and g ( x ) = x n g ( x ) = x n where n n is a positive integer are the building blocks from which all polynomials and rational functions are constructed. To find derivatives of polynomials and rational functions efficiently without resorting to the limit definition of the derivative, we must first develop formulas for differentiating these basic functions. The Constant...