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) = −4x4 − 8x2 + 9x − 6. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −4x4 − 8x2 + 9x − 6x = 1
f′(1) =
2.Easy
xyx = 3

Let f(x) = −x5 + 2x2 − 5x + 2. Find the slope of the graph at x = 3, that is f′(3).

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

Let f(x) = ln(x2 + 2). Find f′(−1).

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

Let f(x) = (2x − 1)4. Find f′(2).

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

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

f(x) = −x2 − x − 4x = −1
b =
6.Hard
xy

Let f(x) = x3 + 1.5x2 − 6x − 6. Find the x-coordinate x of the local maximum.

f(x) = x3 + 1.5x2 − 6x − 6
x =

Answer key

  1. 1. f′(1) = −23
  2. 2. f′(3) = −398
  3. 3. f′(−1) = −0.6667
  4. 4. f′(2) = 216
  5. 5. b = −3
  6. 6. x = −2

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