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

f(x) = −3x3 − 2x2 − 7x − 2x = −2
f′(−2) =
2.Easy
xyx = −1

Let f(x) = 4x4 + 7x2 − x + 9. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 4x4 + 7x2 − x + 9x = −1
f′(−1) =
3.Medium
xyx = 2

Let f(x) = x·sin(2x), with x in radians. Find f′(2).

f(x) = x·sin(2x)x = 2 rad
f′(2) =
4.Medium
xyx = 2

Let f(x) = (2x + 3)4. Find f′(2).

f(x) = (2x + 3)4x = 2
f′(2) =
5.Hard
xyx = 3

The tangent line to f(x) = 0.5x2 + 3x − 2 at x = 3 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 + 3x − 2x = 3
b =
6.Hard
xyx = 3

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

f(x) = −x2 − x + 4x = 3
b =

Answer key

  1. 1. f′(−2) = −35
  2. 2. f′(−1) = −31
  3. 3. f′(2) = −3.371
  4. 4. f′(2) = 2744
  5. 5. b = −6.5
  6. 6. b = 13

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