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) = −2x3 − 2x2 + 9x + 2. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −2x3 − 2x2 + 9x + 2x = 3
f′(3) =
2.Easy
xyx = 2

Let f(x) = −5x5 + 2x2 + 6x + 1. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −5x5 + 2x2 + 6x + 1x = 2
f′(2) =
3.Medium
xyx = −2

Let f(x) = ln(x2 + 4). Find f′(−2).

f(x) = ln(x2 + 4)x = −2
f′(−2) =
4.Medium
xyx = 0

Let f(x) = (−2x + 1)5. Find f′(0).

f(x) = (−2x + 1)5x = 0
f′(0) =
5.Hard
xy

Let f(x) = x3 − 6x2 + 2. Find the x-coordinate x of the local minimum.

f(x) = x3 − 6x2 + 2
x =
6.Hard
xy

Let f(x) = x3 − 3x2 − 9x − 2. Find the x-coordinate x of the local minimum.

f(x) = x3 − 3x2 − 9x − 2
x =

Answer key

  1. 1. f′(3) = −57
  2. 2. f′(2) = −386
  3. 3. f′(−2) = −0.5
  4. 4. f′(0) = −10
  5. 5. x = 4
  6. 6. x = 3

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