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 = −3

Let f(x) = 5x4 − 3x2 + 3x − 7. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = 5x4 − 3x2 + 3x − 7x = −3
f′(−3) =
2.Easy
xyx = −1

Let f(x) = −x4 + 6x2 + 9x − 5. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −x4 + 6x2 + 9x − 5x = −1
f′(−1) =
3.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) =
4.Medium
xyx = 0.5

Let f(x) = x·e2x. Find f′(0.5).

f(x) = x·e2xx = 0.5
f′(0.5) =
5.Hard
xyx = 1

The tangent line to f(x) = 0.5x2 − 3x − 4 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − 3x − 4x = 1
b =
6.Hard
xyx = −1

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

f(x) = −x2 − 4x = −1
b =

Answer key

  1. 1. f′(−3) = −519
  2. 2. f′(−1) = 1
  3. 3. f′(1) = 0.077
  4. 4. f′(0.5) = 5.437
  5. 5. b = −4.5
  6. 6. b = −3

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