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) = x4 + 8x2 − 3x − 1. Find the slope of the graph at x = −2, that is f′(−2).

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

Let f(x) = −3x5 − 5x2 + 8x − 2. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −3x5 − 5x2 + 8x − 2x = 2
f′(2) =
3.Medium
xyx = −1

Let f(x) = (4x + 3)4. Find f′(−1).

f(x) = (4x + 3)4x = −1
f′(−1) =
4.Medium
xyx = −1

Let f(x) = ln(2x2 + 4). Find f′(−1).

f(x) = ln(2x2 + 4)x = −1
f′(−1) =
5.Hard
xy

Let f(x) = x3 − 12x2 + 45x − 3. Find the x-coordinate x of the local minimum.

f(x) = x3 − 12x2 + 45x − 3
x =
6.Hard
xyx = 1

The tangent line to f(x) = 2x2 − 2x − 6 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 2x2 − 2x − 6x = 1
b =

Answer key

  1. 1. f′(−2) = −67
  2. 2. f′(2) = −252
  3. 3. f′(−1) = −16
  4. 4. f′(−1) = −0.6667
  5. 5. x = 5
  6. 6. b = −8

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