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.

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1.Easy
xyx = 3

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

f(x) = x5 + 8x2 + 5x + 8x = 3
f′(3) =
2.Easy
xyx = 2

Let f(x) = 3x3 + 3x2 − 3x + 9. Find the slope of the graph at x = 2, that is f′(2).

f(x) = 3x3 + 3x2 − 3x + 9x = 2
f′(2) =
3.Medium
xyx = 2

Let f(x) = (4x + 5)5. Find f′(2).

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

Let f(x) = (2x − 3)4. Find f′(1).

f(x) = (2x − 3)4x = 1
f′(1) =
5.Hard
xyx = 3

The tangent line to f(x) = 0.5x2 − 4x at x = 3 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − 4xx = 3
b =
6.Hard
xyx = −2

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

f(x) = x2 + 4x − 1x = −2
b =

Answer key

  1. 1. f′(3) = 458
  2. 2. f′(2) = 45
  3. 3. f′(2) = 571220
  4. 4. f′(1) = −8
  5. 5. b = −4.5
  6. 6. b = −5

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