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) = −3x3 − 4x2 − 3x − 1. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −3x3 − 4x2 − 3x − 1x = −3
f′(−3) =
2.Easy
xyx = 2

Let f(x) = −x4 − 4x2 + 3x + 5. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −x4 − 4x2 + 3x + 5x = 2
f′(2) =
3.Medium
xyx = −1

Let f(x) = (−2x + 3)3. Find f′(−1).

f(x) = (−2x + 3)3x = −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
xyx = 1

The tangent line to f(x) = x2 + 5x − 4 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = x2 + 5x − 4x = 1
b =
6.Hard
xy

Let f(x) = x3 − 10.5x2 + 30x + 6. Find the x-coordinate x of the local maximum.

f(x) = x3 − 10.5x2 + 30x + 6
x =

Answer key

  1. 1. f′(−3) = −60
  2. 2. f′(2) = −45
  3. 3. f′(−1) = −150
  4. 4. f′(1) = −2.829
  5. 5. b = −5
  6. 6. x = 2

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