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) = x3 − 8x2 − 4x − 7. Find the slope of the graph at x = 2, that is f′(2).

f(x) = x3 − 8x2 − 4x − 7x = 2
f′(2) =
2.Easy
xyx = −2

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

f(x) = −2x4 − 2x2 + x + 5x = −2
f′(−2) =
3.Medium
xyx = 2

Let f(x) = x·sin(x), with x in radians. Find f′(2).

f(x) = x·sin(x)x = 2 rad
f′(2) =
4.Medium
xyx = 1.5

Let f(x) = x3·ex. Find f′(1.5).

f(x) = x3·exx = 1.5
f′(1.5) =
5.Hard
xy

Let f(x) = x3 − 12x − 4. Find the x-coordinate x of the local maximum.

f(x) = x3 − 12x − 4
x =
6.Hard
xyx = 3

The tangent line to f(x) = 0.5x2 + 4x + 2 at x = 3 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 + 4x + 2x = 3
b =

Answer key

  1. 1. f′(2) = −24
  2. 2. f′(−2) = 73
  3. 3. f′(2) = 0.077
  4. 4. f′(1.5) = 45.38
  5. 5. x = −2
  6. 6. b = −2.5

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