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) = 3x4 − 6x2 + 8x − 2. Find the slope of the graph at x = −1, that is f′(−1).

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

Let f(x) = 3x3 − 6x2 + 5x − 3. Find the slope of the graph at x = 1, that is f′(1).

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

Let f(x) = x2·e0.5x. Find f′(2).

f(x) = x2·e0.5xx = 2
f′(2) =
4.Medium
xyx = 2

Let f(x) = x3·ex. Find f′(2).

f(x) = x3·exx = 2
f′(2) =
5.Hard
xyx = −2

The tangent line to f(x) = x2 + 2x + 5 at x = −2 crosses the y-axis at y = b. Find b.

f(x) = x2 + 2x + 5x = −2
b =
6.Hard
xy

Let f(x) = x3 − 1.5x2 − 6x − 2. Find the x-coordinate x of the local minimum.

f(x) = x3 − 1.5x2 − 6x − 2
x =

Answer key

  1. 1. f′(−1) = 8
  2. 2. f′(1) = 2
  3. 3. f′(2) = 16.31
  4. 4. f′(2) = 147.8
  5. 5. b = 1
  6. 6. x = 2

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