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) = −5x5 − 5x2 + x − 2. Find the slope of the graph at x = −1, that is f′(−1).

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

Let f(x) = 4x3 − 6x2 − x − 5. Find the slope of the graph at x = 1, that is f′(1).

f(x) = 4x3 − 6x2 − x − 5x = 1
f′(1) =
3.Medium
xyx = −2

Let f(x) = ln(2x2 + 4). Find f′(−2).

f(x) = ln(2x2 + 4)x = −2
f′(−2) =
4.Medium
xyx = 1.5

Let f(x) = x2·e2x. Find f′(1.5).

f(x) = x2·e2xx = 1.5
f′(1.5) =
5.Hard
xy

Let f(x) = x3 − 4.5x2 − 4. Find the x-coordinate x of the local minimum.

f(x) = x3 − 4.5x2 − 4
x =
6.Hard
xyx = 2

The tangent line to f(x) = 0.5x2 − 2x at x = 2 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − 2xx = 2
b =

Answer key

  1. 1. f′(−1) = −14
  2. 2. f′(1) = −1
  3. 3. f′(−2) = −0.6667
  4. 4. f′(1.5) = 150.6
  5. 5. x = 3
  6. 6. b = −2

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