Derivatives worksheet with answers

Free printable Derivatives worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
xyx = −3

Let f(x) = 2x5 + 7x2 − 5x − 3. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = 2x5 + 7x2 − 5x − 3x = −3
f′(−3) =
2.Easy
xyx = −2

Let f(x) = −3x5 − 2x2 − 5x − 7. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −3x5 − 2x2 − 5x − 7x = −2
f′(−2) =
3.Medium
xyx = 2

Let f(x) = x2·e0.5x. Find f′(2).

f(x) = x2·e0.5xx = 2
f′(2) =
4.Medium
xyx = 2

Let f(x) = (2x − 3)3. Find f′(2).

f(x) = (2x − 3)3x = 2
f′(2) =
5.Hard
xyx = −2

The tangent line to f(x) = −x2 − 2x at x = −2 crosses the y-axis at y = b. Find b.

f(x) = −x2 − 2xx = −2
b =
6.Hard
xyx = 1

The tangent line to f(x) = −x2 + 5x + 5 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = −x2 + 5x + 5x = 1
b =

Answer key

  1. 1. f′(−3) = 763
  2. 2. f′(−2) = −237
  3. 3. f′(2) = 16.31
  4. 4. f′(2) = 6
  5. 5. b = 4
  6. 6. b = 6

Full step-by-step solutions: practise this topic on examproblems.com.