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 = 2

Let f(x) = −x5 − 4x2 − 8x − 9. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −x5 − 4x2 − 8x − 9x = 2
f′(2) =
2.Easy
xyx = −1

Let f(x) = 2x3 − 9x2 − 9. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 2x3 − 9x2 − 9x = −1
f′(−1) =
3.Medium
xyx = 1.5

Let f(x) = x·e0.5x. Find f′(1.5).

f(x) = x·e0.5xx = 1.5
f′(1.5) =
4.Medium
xyx = 0.5

Let f(x) = x3·e−0.5x. Find f′(0.5).

f(x) = x3·e−0.5xx = 0.5
f′(0.5) =
5.Hard
xyx = −2

The tangent line to f(x) = x2 − 4x at x = −2 crosses the y-axis at y = b. Find b.

f(x) = x2 − 4xx = −2
b =
6.Hard
xyx = −1

The tangent line to f(x) = 0.5x2 + 2x − 6 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 + 2x − 6x = −1
b =

Answer key

  1. 1. f′(2) = −104
  2. 2. f′(−1) = 24
  3. 3. f′(1.5) = 3.705
  4. 4. f′(0.5) = 0.5354
  5. 5. b = −4
  6. 6. b = −6.5

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