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) = 2x3 − 8x2 + 2x + 1. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = 2x3 − 8x2 + 2x + 1x = −3
f′(−3) =
2.Easy
xyx = −2

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

f(x) = 2x5 − 5x2 − 5x − 2x = −2
f′(−2) =
3.Medium
xyx = 1

Let f(x) = x3·e2x. Find f′(1).

f(x) = x3·e2xx = 1
f′(1) =
4.Medium
xyx = 1

Let f(x) = x·sin(3x), with x in radians. Find f′(1).

f(x) = x·sin(3x)x = 1 rad
f′(1) =
5.Hard
xy

Let f(x) = x3 − 12x2 + 36x − 3. Find the x-coordinate x of the local minimum.

f(x) = x3 − 12x2 + 36x − 3
x =
6.Hard
xy

Let f(x) = x3 + 10.5x2 + 36x. Find the x-coordinate x of the local maximum.

f(x) = x3 + 10.5x2 + 36x
x =

Answer key

  1. 1. f′(−3) = 104
  2. 2. f′(−2) = 175
  3. 3. f′(1) = 36.95
  4. 4. f′(1) = −2.829
  5. 5. x = 6
  6. 6. x = −4

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