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) = −x5 − 7x2 + 4x − 8. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −x5 − 7x2 + 4x − 8x = 3
f′(3) =
2.Easy
xyx = −2

Let f(x) = −3x4 + x2 − 5x − 4. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −3x4 + x2 − 5x − 4x = −2
f′(−2) =
3.Medium
xyx = 1

Let f(x) = x·ex. Find f′(1).

f(x) = x·exx = 1
f′(1) =
4.Medium
xyx = 0

Let f(x) = (3x − 3)3. Find f′(0).

f(x) = (3x − 3)3x = 0
f′(0) =
5.Hard
xyx = 3

The tangent line to f(x) = 0.5x2 + 4x + 4 at x = 3 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 + 4x + 4x = 3
b =
6.Hard
xy

Let f(x) = x3 − 9x2 + 24x + 3. Find the x-coordinate x of the local minimum.

f(x) = x3 − 9x2 + 24x + 3
x =

Answer key

  1. 1. f′(3) = −443
  2. 2. f′(−2) = 87
  3. 3. f′(1) = 5.437
  4. 4. f′(0) = 81
  5. 5. b = −0.5
  6. 6. x = 4

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