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 + 3x2 + 5x − 2. Find the slope of the graph at x = 2, that is f′(2).

f(x) = 2x5 + 3x2 + 5x − 2x = 2
f′(2) =
2.Easy
xyx = 1

Let f(x) = −3x5 − 8x2 − 5x − 3. Find the slope of the graph at x = 1, that is f′(1).

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

Let f(x) = ln(x2 + 1). Find f′(1).

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

Let f(x) = x·ex. Find f′(2).

f(x) = x·exx = 2
f′(2) =
5.Hard
xyx = 2

The tangent line to f(x) = 3x2 + 4x − 6 at x = 2 crosses the y-axis at y = b. Find b.

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

The tangent line to f(x) = 3x2 + 4x − 5 at x = 2 crosses the y-axis at y = b. Find b.

f(x) = 3x2 + 4x − 5x = 2
b =

Answer key

  1. 1. f′(2) = 177
  2. 2. f′(1) = −36
  3. 3. f′(1) = 1
  4. 4. f′(2) = 22.17
  5. 5. b = −18
  6. 6. b = −17

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