Differentiation Practice Problems for AP Calculus
Review the following concepts if needed:
- Definition of the Derivative of a Function for AP Calculus
- Power Rule for AP Calculus
- The Sum, Difference, Product, and Quotient Rules for AP Calculus
- The Chain Rule for AP Calculus
- Derivatives of Trigonometric Functions for AP Calculus
- Derivatives of Inverse Trigonometric Functions for AP Calculus
- Derivatives of Exponential and Logarithmic Functions for AP Calculus
- Procedure for Implicit Differentiation for AP Calculus
- Approximating a Derivative for AP Calculus
- Derivatives of Inverse Functions for AP Calculus
- Higher Order Derivatives for AP Calculus
- L'Hopital's Rule for Indeterminate Forms Higher Order Derivatives for AP Calculus
Part A—The use of a calculator is not allowed.
Find the derivative of each of the following functions.
- y = 6x5 – x + 10
- f (x ) = (3x – 2)5(x2 – 1)
- y = 10 cot(2x – 1)
- y = 3x sec(3x)
- y = 10 cos[sin(x2 – 4)]
- y = 8 cos–1(2x )
- y = 3e5 +4xex
- y = ln(x2 +3)
Part B—Calculators are allowed.
- Find , if x2 + y3 =10 – 5xy.
- The graph of a function f on [1, 5] is shown in Figure 6.9–1. Find the approximate value of f '(4).
- Let f be a continuous and differentiable function. Selected values of f are shown below. Find the approximate value of f ' at x =2.
- If f (x) = x5 + 3x – 8, find ( f –1)'(–8).
- Write an equation of the tangent to the curve y = ln x at x = e.
- If y = 2x sin x, find at x = .
- If the function f (x)=(x – 1)2/3 + 2, find all points where f is not differentiable.
- Write an equation of the normal line to the curve x cos y = 1 at (2, ).
(Calculator) indicates that calculators are permitted.
- Find .
- If f (x)= cos2(π – x ), find f '(0).
- Find .
- (Calculator) Let f be a continuous and differentiable function. Selected values of f are shown below. Find the approximate value of f ' at x = 2.
- (Calculator) If determine if f (x) is continuous at (x = 3). Explain why or why not?
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