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) = −2x4 − 8x2 + x + 9. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −2x4 − 8x2 + x + 9x = −3
f′(−3) =
2.Easy
xyx = −3

Let f(x) = 5x4 + 7x2 − 2x + 7. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = 5x4 + 7x2 − 2x + 7x = −3
f′(−3) =
3.Medium
xyx = 0.5

Let f(x) = x3·e0.5x. Find f′(0.5).

f(x) = x3·e0.5xx = 0.5
f′(0.5) =
4.Medium
xyx = 1

Let f(x) = ln(3x2 + 1). Find f′(1).

f(x) = ln(3x2 + 1)x = 1
f′(1) =
5.Hard
xyx = 1

The tangent line to f(x) = −x2 + 5x − 2 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = −x2 + 5x − 2x = 1
b =
6.Hard
xy

Let f(x) = x3 + 1.5x2 − 4. Find the x-coordinate x of the local maximum.

f(x) = x3 + 1.5x2 − 4
x =

Answer key

  1. 1. f′(−3) = 265
  2. 2. f′(−3) = −584
  3. 3. f′(0.5) = 1.043
  4. 4. f′(1) = 1.5
  5. 5. b = −1
  6. 6. x = −1

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