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 − 9x2 + 7x. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −5x3 − 9x2 + 7xx = 2
f′(2) =
2.Easy
xyx = 2

Let f(x) = 5x3 + 4x2 + 4x + 1. Find the slope of the graph at x = 2, that is f′(2).

f(x) = 5x3 + 4x2 + 4x + 1x = 2
f′(2) =
3.Medium
xyx = 1

Let f(x) = (−2x − 3)5. Find f′(1).

f(x) = (−2x − 3)5x = 1
f′(1) =
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
xyx = −1

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

f(x) = −x2 − 3x = −1
b =
6.Hard
xy

Let f(x) = x3 + 7.5x2 + 12x − 1. Find the x-coordinate x of the local minimum.

f(x) = x3 + 7.5x2 + 12x − 1
x =

Answer key

  1. 1. f′(2) = −89
  2. 2. f′(2) = 80
  3. 3. f′(1) = −6250
  4. 4. f′(0.5) = 1.382
  5. 5. b = −2
  6. 6. x = −1

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