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) = −x3 − 5x2 − 7x. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −x3 − 5x2 − 7xx = 3
f′(3) =
2.Easy
xyx = 1

Let f(x) = 3x5 + 8x2 + 9x + 5. Find the slope of the graph at x = 1, that is f′(1).

f(x) = 3x5 + 8x2 + 9x + 5x = 1
f′(1) =
3.Medium
xyx = 1

Let f(x) = x3·e−x. Find f′(1).

f(x) = x3·e−xx = 1
f′(1) =
4.Medium
xyx = 0

Let f(x) = (−2x + 3)4. Find f′(0).

f(x) = (−2x + 3)4x = 0
f′(0) =
5.Hard
xy

Let f(x) = x3 − 15x2 + 63x + 2. Find the x-coordinate x of the local maximum.

f(x) = x3 − 15x2 + 63x + 2
x =
6.Hard
xyx = −2

The tangent line to f(x) = 0.5x2 − 3 at x = −2 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − 3x = −2
b =

Answer key

  1. 1. f′(3) = −64
  2. 2. f′(1) = 40
  3. 3. f′(1) = 0.7358
  4. 4. f′(0) = −216
  5. 5. x = 3
  6. 6. b = −5

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