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) = x3 + 2x2 + 2x − 1. Find the slope of the graph at x = −2, that is f′(−2).

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

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

f(x) = x4 − 3x2 + x + 6x = −2
f′(−2) =
3.Medium
xyx = 2

Let f(x) = x3·e−x. Find f′(2).

f(x) = x3·e−xx = 2
f′(2) =
4.Medium
xyx = 1.5

Let f(x) = x2·e−x. Find f′(1.5).

f(x) = x2·e−xx = 1.5
f′(1.5) =
5.Hard
xyx = 1

The tangent line to f(x) = x2 + 3x + 6 at x = 1 crosses the y-axis at y = b. Find b.

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

The tangent line to f(x) = 3x2 + x at x = −1 crosses the y-axis at y = b. Find b.

f(x) = 3x2 + xx = −1
b =

Answer key

  1. 1. f′(−2) = 6
  2. 2. f′(−2) = −19
  3. 3. f′(2) = 0.5413
  4. 4. f′(1.5) = 0.1673
  5. 5. b = 5
  6. 6. b = −3

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