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 = 1

Let f(x) = −2x4 − 6x2 − 2x − 6. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −2x4 − 6x2 − 2x − 6x = 1
f′(1) =
2.Easy
xyx = 3

Let f(x) = −2x4 − 2x2 + 7x + 6. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −2x4 − 2x2 + 7x + 6x = 3
f′(3) =
3.Medium
xyx = 0.5

Let f(x) = x2·ex. Find f′(0.5).

f(x) = x2·exx = 0.5
f′(0.5) =
4.Medium
xyx = −1

Let f(x) = (4x + 1)4. Find f′(−1).

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

The tangent line to f(x) = 0.5x2 − 5x − 6 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − 5x − 6x = −1
b =
6.Hard
xyx = −2

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

f(x) = −x2 − x − 1x = −2
b =

Answer key

  1. 1. f′(1) = −22
  2. 2. f′(3) = −221
  3. 3. f′(0.5) = 2.061
  4. 4. f′(−1) = −432
  5. 5. b = −6.5
  6. 6. b = 3

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