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) = 3x4 + 9x2 + 9x + 8. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 3x4 + 9x2 + 9x + 8x = −1
f′(−1) =
2.Easy
xyx = −3

Let f(x) = −5x3 + 7x2 + 5x + 8. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −5x3 + 7x2 + 5x + 8x = −3
f′(−3) =
3.Medium
xyx = 1.5

Let f(x) = x3·ex. Find f′(1.5).

f(x) = x3·exx = 1.5
f′(1.5) =
4.Medium
xyx = 2

Let f(x) = ln(2x2 + 5). Find f′(2).

f(x) = ln(2x2 + 5)x = 2
f′(2) =
5.Hard
xyx = 1

The tangent line to f(x) = −x2 − 4x + 3 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = −x2 − 4x + 3x = 1
b =
6.Hard
xy

Let f(x) = x3 − 9x2 + 24x − 2. Find the x-coordinate x of the local maximum.

f(x) = x3 − 9x2 + 24x − 2
x =

Answer key

  1. 1. f′(−1) = −21
  2. 2. f′(−3) = −172
  3. 3. f′(1.5) = 45.38
  4. 4. f′(2) = 0.6154
  5. 5. b = 4
  6. 6. x = 2

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