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) = −x3 + 8x2 + 5x − 4. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −x3 + 8x2 + 5x − 4x = −3
f′(−3) =
2.Easy
xyx = 2

Let f(x) = 3x4 − 5x2 − 6x − 6. Find the slope of the graph at x = 2, that is f′(2).

f(x) = 3x4 − 5x2 − 6x − 6x = 2
f′(2) =
3.Medium
xyx = 1

Let f(x) = x3·e−x. Find f′(1).

f(x) = x3·e−xx = 1
f′(1) =
4.Medium
xyx = 1.5

Let f(x) = x·sin(2x), with x in radians. Find f′(1.5).

f(x) = x·sin(2x)x = 1.5 rad
f′(1.5) =
5.Hard
xyx = 1

The tangent line to f(x) = 0.5x2 − x − 6 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − x − 6x = 1
b =
6.Hard
xyx = 2

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

f(x) = 0.5x2 + x − 2x = 2
b =

Answer key

  1. 1. f′(−3) = −70
  2. 2. f′(2) = 70
  3. 3. f′(1) = 0.7358
  4. 4. f′(1.5) = −2.829
  5. 5. b = −6.5
  6. 6. b = −4

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