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 = −1

Let f(x) = −2x5 − x2 − 8x + 3. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −2x5 − x2 − 8x + 3x = −1
f′(−1) =
2.Easy
xyx = 2

Let f(x) = 4x4 − 5x2 − 9x − 6. Find the slope of the graph at x = 2, that is f′(2).

f(x) = 4x4 − 5x2 − 9x − 6x = 2
f′(2) =
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 = 0.5

Let f(x) = x3·e−0.5x. Find f′(0.5).

f(x) = x3·e−0.5xx = 0.5
f′(0.5) =
5.Hard
xy

Let f(x) = x3 − 1.5x2 + 5. Find the x-coordinate x of the local minimum.

f(x) = x3 − 1.5x2 + 5
x =
6.Hard
xy

Let f(x) = x3 − 12x − 5. Find the x-coordinate x of the local maximum.

f(x) = x3 − 12x − 5
x =

Answer key

  1. 1. f′(−1) = −16
  2. 2. f′(2) = 99
  3. 3. f′(2) = −3.371
  4. 4. f′(0.5) = 0.5354
  5. 5. x = 1
  6. 6. x = −2

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