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) = −x4 + 2x2 − 7x + 7. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −x4 + 2x2 − 7x + 7x = −3
f′(−3) =
2.Easy
xyx = −3

Let f(x) = −3x3 − 6x2 − 5x − 4. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −3x3 − 6x2 − 5x − 4x = −3
f′(−3) =
3.Medium
xyx = 1

Let f(x) = x·e−0.5x. Find f′(1).

f(x) = x·e−0.5xx = 1
f′(1) =
4.Medium
xyx = 1

Let f(x) = (3x + 5)5. Find f′(1).

f(x) = (3x + 5)5x = 1
f′(1) =
5.Hard
xyx = 1

The tangent line to f(x) = 2x2 − 4x − 5 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 2x2 − 4x − 5x = 1
b =
6.Hard
xyx = −2

The tangent line to f(x) = −x2 − 5x + 5 at x = −2 crosses the y-axis at y = b. Find b.

f(x) = −x2 − 5x + 5x = −2
b =

Answer key

  1. 1. f′(−3) = 89
  2. 2. f′(−3) = −50
  3. 3. f′(1) = 0.3033
  4. 4. f′(1) = 61440
  5. 5. b = −7
  6. 6. b = 9

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