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) = 5x4 + 2x2 + 4x − 3. Find the slope of the graph at x = 1, that is f′(1).

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

Let f(x) = 5x5 − 2x2 + 9x − 6. Find the slope of the graph at x = 3, that is f′(3).

f(x) = 5x5 − 2x2 + 9x − 6x = 3
f′(3) =
3.Medium
xyx = 1

Let f(x) = ln(3x2 + 1). Find f′(1).

f(x) = ln(3x2 + 1)x = 1
f′(1) =
4.Medium
xyx = 1

Let f(x) = x·e2x. Find f′(1).

f(x) = x·e2xx = 1
f′(1) =
5.Hard
xy

Let f(x) = x3 − 9x2 + 15x − 2. Find the x-coordinate x of the local minimum.

f(x) = x3 − 9x2 + 15x − 2
x =
6.Hard
xyx = −1

The tangent line to f(x) = 0.5x2 − 4x + 4 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − 4x + 4x = −1
b =

Answer key

  1. 1. f′(1) = 28
  2. 2. f′(3) = 2022
  3. 3. f′(1) = 1.5
  4. 4. f′(1) = 22.17
  5. 5. x = 5
  6. 6. b = 3.5

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