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) = 5x4 − 9x2 − 9x. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = 5x4 − 9x2 − 9xx = −3
f′(−3) =
2.Easy
xyx = −1

Let f(x) = −x3 + 2x2 − 3x − 4. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −x3 + 2x2 − 3x − 4x = −1
f′(−1) =
3.Medium
xyx = 0.5

Let f(x) = x·sin(x), with x in radians. Find f′(0.5).

f(x) = x·sin(x)x = 0.5 rad
f′(0.5) =
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) = x2 + x + 4 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = x2 + x + 4x = 1
b =
6.Hard
xyx = 1

The tangent line to f(x) = 2x2 − 3x + 6 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 2x2 − 3x + 6x = 1
b =

Answer key

  1. 1. f′(−3) = −495
  2. 2. f′(−1) = −10
  3. 3. f′(0.5) = 0.9182
  4. 4. f′(−1) = 240
  5. 5. b = 3
  6. 6. b = 4

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