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 = −1

Let f(x) = 2x4 + 6x2 + 9x − 3. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 2x4 + 6x2 + 9x − 3x = −1
f′(−1) =
2.Easy
xyx = −3

Let f(x) = −2x3 + 7x2 + 9x + 5. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −2x3 + 7x2 + 9x + 5x = −3
f′(−3) =
3.Medium
xyx = −1

Let f(x) = (−2x + 1)5. Find f′(−1).

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

Let f(x) = (−2x − 1)4. Find f′(−1).

f(x) = (−2x − 1)4x = −1
f′(−1) =
5.Hard
xyx = −1

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

f(x) = −x2 + 5xx = −1
b =
6.Hard
xyx = 3

The tangent line to f(x) = 3x2 + 3x − 5 at x = 3 crosses the y-axis at y = b. Find b.

f(x) = 3x2 + 3x − 5x = 3
b =

Answer key

  1. 1. f′(−1) = −11
  2. 2. f′(−3) = −87
  3. 3. f′(−1) = −810
  4. 4. f′(−1) = −8
  5. 5. b = 1
  6. 6. b = −32

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