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) = −5x5 + 7x2 + 9x − 1. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −5x5 + 7x2 + 9x − 1x = 2
f′(2) =
2.Easy
xyx = 1

Let f(x) = 2x5 + 2x2 − 7x + 6. Find the slope of the graph at x = 1, that is f′(1).

f(x) = 2x5 + 2x2 − 7x + 6x = 1
f′(1) =
3.Medium
xyx = 0.5

Let f(x) = x·sin(3x), with x in radians. Find f′(0.5).

f(x) = x·sin(3x)x = 0.5 rad
f′(0.5) =
4.Medium
xyx = −2

Let f(x) = ln(3x2 + 5). Find f′(−2).

f(x) = ln(3x2 + 5)x = −2
f′(−2) =
5.Hard
xyx = 1

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

f(x) = 2x2 + 5xx = 1
b =
6.Hard
xyx = 3

The tangent line to f(x) = 2x2 + 5x at x = 3 crosses the y-axis at y = b. Find b.

f(x) = 2x2 + 5xx = 3
b =

Answer key

  1. 1. f′(2) = −363
  2. 2. f′(1) = 7
  3. 3. f′(0.5) = 1.104
  4. 4. f′(−2) = −0.7059
  5. 5. b = −2
  6. 6. b = −18

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