By William Ma — McGraw-Hill Professional

Updated on Oct 24, 2011

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

### Practice Problems

**Part A—The use of a calculator is not allowed.**

Find the derivative of each of the following functions.

*y*= 6*x*^{5}–*x*+ 10*f*(*x*) = (3*x*– 2)^{5}(*x*^{2}– 1)*y*= 10 cot(2*x*– 1)*y*= 3*x*sec(3*x*)*y*= 10 cos[sin(*x*^{2}– 4)]*y*= 8 cos^{–1}(2x )*y*= 3*e*^{5}+4*xe*^{x}*y*= ln(*x*^{2}+3)

**Part B—Calculators are allowed.**

- Find , if
*x*^{2}+*y*^{3}=10 – 5*xy*. - 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*) =*x*^{5}+ 3*x*– 8, find (*f*^{–1})'(–8). - Write an equation of the tangent to the curve
*y*= ln*x*at*x*=*e*. - If
*y*= 2*x*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*)= cos^{2}(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?

From 5 Steps to a 5 AP Calculus AB and BC. Copyright © 2010 by The McGraw-Hill Companies. All Rights Reserved.

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