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) = −5x3 + 3x2 − 3x + 1. Find the slope of the graph at x = 2, that is f′(2).

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

Let f(x) = −x3 + 4x2 − 3x + 2. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −x3 + 4x2 − 3x + 2x = −2
f′(−2) =
3.Medium
xyx = 3

Let f(x) = ln(x2 + 5). Find f′(3).

f(x) = ln(x2 + 5)x = 3
f′(3) =
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 − 13.5x2 + 54x. Find the x-coordinate x of the local maximum.

f(x) = x3 − 13.5x2 + 54x
x =
6.Hard
xyx = 2

The tangent line to f(x) = 0.5x2 + 2x + 5 at x = 2 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 + 2x + 5x = 2
b =

Answer key

  1. 1. f′(2) = −51
  2. 2. f′(−2) = −31
  3. 3. f′(3) = 0.4286
  4. 4. f′(0) = −216
  5. 5. x = 3
  6. 6. b = 3

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