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) = 5x4 + 8x2 − 7x − 1. Find the slope of the graph at x = 2, that is f′(2).

f(x) = 5x4 + 8x2 − 7x − 1x = 2
f′(2) =
2.Easy
xyx = −1

Let f(x) = −5x3 + 9x2 − 7x. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −5x3 + 9x2 − 7xx = −1
f′(−1) =
3.Medium
xyx = 1.5

Let f(x) = x·e−0.5x. Find f′(1.5).

f(x) = x·e−0.5xx = 1.5
f′(1.5) =
4.Medium
xyx = 1

Let f(x) = x·sin(2x), with x in radians. Find f′(1).

f(x) = x·sin(2x)x = 1 rad
f′(1) =
5.Hard
xy

Let f(x) = x3 − 1.5x2 − 6x − 3. Find the x-coordinate x of the local maximum.

f(x) = x3 − 1.5x2 − 6x − 3
x =
6.Hard
xyx = −1

The tangent line to f(x) = 3x2 − 2x − 2 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = 3x2 − 2x − 2x = −1
b =

Answer key

  1. 1. f′(2) = 185
  2. 2. f′(−1) = −40
  3. 3. f′(1.5) = 0.1181
  4. 4. f′(1) = 0.077
  5. 5. x = −1
  6. 6. b = −5

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