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 = −2

Let f(x) = −4x5 − 5x2 + 5x + 8. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −4x5 − 5x2 + 5x + 8x = −2
f′(−2) =
2.Easy
xyx = 1

Let f(x) = 4x5 + 5x2 + 4x + 8. Find the slope of the graph at x = 1, that is f′(1).

f(x) = 4x5 + 5x2 + 4x + 8x = 1
f′(1) =
3.Medium
xyx = 1

Let f(x) = (2x + 5)4. Find f′(1).

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

Let f(x) = ln(x2 + 5). Find f′(−1).

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

Let f(x) = x3 − 15x2 + 63x + 4. Find the x-coordinate x of the local minimum.

f(x) = x3 − 15x2 + 63x + 4
x =
6.Hard
xy

Let f(x) = x3 − 9x2 + 15x + 6. Find the x-coordinate x of the local minimum.

f(x) = x3 − 9x2 + 15x + 6
x =

Answer key

  1. 1. f′(−2) = −295
  2. 2. f′(1) = 34
  3. 3. f′(1) = 2744
  4. 4. f′(−1) = −0.3333
  5. 5. x = 7
  6. 6. x = 5

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