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Differentiation Practice Problems for AP Calculus

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By — McGraw-Hill Professional
Updated on Oct 24, 2011

Review the following concepts if needed:

Practice Problems

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

Find the derivative of each of the following functions.

  1. y = 6x5x + 10
  2. f (x ) = (3x – 2)5(x2 – 1)
  3. y = 10 cot(2x – 1)
  4. y = 3x sec(3x)
  5. y = 10 cos[sin(x2 – 4)]
  6. y = 8 cos–1(2x )
  7. y = 3e5 +4xex
  8. y = ln(x2 +3)

Part B—Calculators are allowed.

  1. Find , if x2 + y3 =10 – 5xy.
  2. The graph of a function f on [1, 5] is shown in Figure 6.9–1. Find the approximate value of f '(4).
  3. Let f be a continuous and differentiable function. Selected values of f are shown below. Find the approximate value of f ' at x =2.
  4. Practice Problems

  5. If f (x) = x5 + 3x – 8, find ( f –1)'(–8).
  6. Write an equation of the tangent to the curve y = ln x at x = e.
  7. If y = 2x sin x, find at x = .
  8. If the function f (x)=(x – 1)2/3 + 2, find all points where f is not differentiable.
  9. Write an equation of the normal line to the curve x cos y = 1 at (2, ).

 

(Calculator) indicates that calculators are permitted.

  1. Find .
  2. If f (x)= cos2(π – x ), find f '(0).
  3. Find .
  4. (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.
  5. (Calculator) If determine if f (x) is continuous at (x = 3). Explain why or why not?
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