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) = 2x5 + 9x2 + 3x − 1. Find the slope of the graph at x = −2, that is f′(−2).

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

Let f(x) = −4x5 − 5x2 − 7x + 8. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −4x5 − 5x2 − 7x + 8x = 1
f′(1) =
3.Medium
xyx = 3

Let f(x) = ln(2x2 + 2). Find f′(3).

f(x) = ln(2x2 + 2)x = 3
f′(3) =
4.Medium
xyx = 0.5

Let f(x) = x·sin(2x), with x in radians. Find f′(0.5).

f(x) = x·sin(2x)x = 0.5 rad
f′(0.5) =
5.Hard
xy

Let f(x) = x3 − 9x2 + 15x + 6. Find the x-coordinate x of the local maximum.

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

The tangent line to f(x) = 2x2 + 3x − 2 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = 2x2 + 3x − 2x = −1
b =

Answer key

  1. 1. f′(−2) = 127
  2. 2. f′(1) = −37
  3. 3. f′(3) = 0.6
  4. 4. f′(0.5) = 1.382
  5. 5. x = 1
  6. 6. b = −4

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