Differentiation formula pdf

3 Derivatives • Introduction • 3.1 Defining the Derivative • 3.2 The Derivative as a Function • 3.3 Differentiation Rules • 3.4 Derivatives as Rates of Change • 3.5 Derivatives of Trigonometric Functions • 3.6 The Chain Rule • 3.7 Derivatives of Inverse Functions • 3.8 Implicit Differentiation • 3.9 Derivatives of Exponential and Logarithmic Functions • 4 Applications of Derivatives • Introduction • 4.1 Related Rates • 4.2 Linear Approximations and Differentials • 4.3 Maxima and Minima • 4.4 The Mean Value Theorem • 4.5 Derivatives and the Shape of a Graph • 4.6 Limits at Infinity and Asymptotes • 4.7 Applied Optimization Problems • 4.8 L’Hôpital’s Rule • 4.9 Newton’s Method • 4.10 Antiderivatives • 5 Integration • Introduction • 5.1 Approximating Areas • 5.2 The Definite Integral • 5.3 The Fundamental Theorem of Calculus • 5.4 Integration Formulas and the Net Change Theorem • 5.5 Substitution • 5.6 Integrals Involving Exponential and Logarithmic Functions • 5.7 Integrals Resulting in Inverse Trigonometric Functions • 6 Applications of Integration • Introduction • 6.1 Areas between Curves • 6.2 Determining Volumes by Slicing • 6.3 Volumes of Revolution: Cylindrical Shells • 6.4 Arc Length of a Curve and Surface Area • 6.5 Physical Applications • 6.6 Moments and Centers of Mass • 6.7 Integrals, Exponential Functions, and Logarithms • 6.8 Exponential Growth and Decay • 6.9 Calculus of the Hyperbolic Functions • Learning Objectives • 3.3.1 State the constant, constant multipl...

3 Derivatives • Introduction • 3.1 Defining the Derivative • 3.2 The Derivative as a Function • 3.3 Differentiation Rules • 3.4 Derivatives as Rates of Change • 3.5 Derivatives of Trigonometric Functions • 3.6 The Chain Rule • 3.7 Derivatives of Inverse Functions • 3.8 Implicit Differentiation • 3.9 Derivatives of Exponential and Logarithmic Functions • 4 Applications of Derivatives • Introduction • 4.1 Related Rates • 4.2 Linear Approximations and Differentials • 4.3 Maxima and Minima • 4.4 The Mean Value Theorem • 4.5 Derivatives and the Shape of a Graph • 4.6 Limits at Infinity and Asymptotes • 4.7 Applied Optimization Problems • 4.8 L’Hôpital’s Rule • 4.9 Newton’s Method • 4.10 Antiderivatives • 5 Integration • Introduction • 5.1 Approximating Areas • 5.2 The Definite Integral • 5.3 The Fundamental Theorem of Calculus • 5.4 Integration Formulas and the Net Change Theorem • 5.5 Substitution • 5.6 Integrals Involving Exponential and Logarithmic Functions • 5.7 Integrals Resulting in Inverse Trigonometric Functions • 6 Applications of Integration • Introduction • 6.1 Areas between Curves • 6.2 Determining Volumes by Slicing • 6.3 Volumes of Revolution: Cylindrical Shells • 6.4 Arc Length of a Curve and Surface Area • 6.5 Physical Applications • 6.6 Moments and Centers of Mass • 6.7 Integrals, Exponential Functions, and Logarithms • 6.8 Exponential Growth and Decay • 6.9 Calculus of the Hyperbolic Functions • Learning Objectives • 3.3.1 State the constant, constant multipl...