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) = −4x4 + 4x2 + 5x − 8. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −4x4 + 4x2 + 5x − 8x = 1
f′(1) =
2.Easy
xyx = 3

Let f(x) = 5x4 + x2 − 2x − 8. Find the slope of the graph at x = 3, that is f′(3).

f(x) = 5x4 + x2 − 2x − 8x = 3
f′(3) =
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 = 1.5

Let f(x) = x3·e−x. Find f′(1.5).

f(x) = x3·e−xx = 1.5
f′(1.5) =
5.Hard
xyx = −1

The tangent line to f(x) = −x2 − 5x − 6 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = −x2 − 5x − 6x = −1
b =
6.Hard
xyx = 2

The tangent line to f(x) = 0.5x2 − 6 at x = 2 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − 6x = 2
b =

Answer key

  1. 1. f′(1) = −3
  2. 2. f′(3) = 544
  3. 3. f′(1) = 0.077
  4. 4. f′(1.5) = 0.7531
  5. 5. b = −5
  6. 6. b = −8

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