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

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

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

f(x) = 2x4 − x2 + 2x − 2x = −1
f′(−1) =
3.Medium
xyx = −2

Let f(x) = ln(3x2 + 5). Find f′(−2).

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

Let f(x) = (−2x − 3)3. Find f′(−1).

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

The tangent line to f(x) = x2 − 5x + 4 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = x2 − 5x + 4x = 1
b =
6.Hard
xy

Let f(x) = x3 + 6x2 + 9x − 4. Find the x-coordinate x of the local maximum.

f(x) = x3 + 6x2 + 9x − 4
x =

Answer key

  1. 1. f′(1) = 26
  2. 2. f′(−1) = −4
  3. 3. f′(−2) = −0.7059
  4. 4. f′(−1) = −6
  5. 5. b = 3
  6. 6. x = −3

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