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

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

Let f(x) = 5x5 + 6x2 − 5x − 3. Find the slope of the graph at x = −1, that is f′(−1).

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

Let f(x) = x·sin(2x), with x in radians. Find f′(1).

f(x) = x·sin(2x)x = 1 rad
f′(1) =
4.Medium
xyx = 1

Let f(x) = ln(x2 + 2). Find f′(1).

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

The tangent line to f(x) = 3x2 + 2x − 4 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = 3x2 + 2x − 4x = −1
b =
6.Hard
xy

Let f(x) = x3 − 15x2 + 63x. Find the x-coordinate x of the local maximum.

f(x) = x3 − 15x2 + 63x
x =

Answer key

  1. 1. f′(2) = −61
  2. 2. f′(−1) = 8
  3. 3. f′(1) = 0.077
  4. 4. f′(1) = 0.6667
  5. 5. b = −7
  6. 6. x = 3

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