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) = −5x4 + 3x2 − x − 4. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −5x4 + 3x2 − x − 4x = 3
f′(3) =
2.Easy
xyx = −1

Let f(x) = 2x5 + 4x2 + 3x − 2. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 2x5 + 4x2 + 3x − 2x = −1
f′(−1) =
3.Medium
xyx = 1

Let f(x) = ln(3x2 + 2). Find f′(1).

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

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

f(x) = x·sin(x)x = 2 rad
f′(2) =
5.Hard
xyx = 1

The tangent line to f(x) = 2x2 + 3x + 6 at x = 1 crosses the y-axis at y = b. Find b.

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

Let f(x) = x3 − 4.5x2 + 6x − 2. Find the x-coordinate x of the local maximum.

f(x) = x3 − 4.5x2 + 6x − 2
x =

Answer key

  1. 1. f′(3) = −523
  2. 2. f′(−1) = 5
  3. 3. f′(1) = 1.2
  4. 4. f′(2) = 0.077
  5. 5. b = 4
  6. 6. x = 1

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