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 + 3x2 − 4x + 2. Find the slope of the graph at x = 1, that is f′(1).

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

Let f(x) = −5x3 − 3x2 − 6x + 8. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −5x3 − 3x2 − 6x + 8x = −1
f′(−1) =
3.Medium
xyx = 2

Let f(x) = x2·e−0.5x. Find f′(2).

f(x) = x2·e−0.5xx = 2
f′(2) =
4.Medium
xyx = 2

Let f(x) = x·sin(3x), with x in radians. Find f′(2).

f(x) = x·sin(3x)x = 2 rad
f′(2) =
5.Hard
xyx = 2

The tangent line to f(x) = 0.5x2 − x − 3 at x = 2 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − x − 3x = 2
b =
6.Hard
xyx = 3

The tangent line to f(x) = 0.5x2 − x − 6 at x = 3 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − x − 6x = 3
b =

Answer key

  1. 1. f′(1) = −10
  2. 2. f′(−1) = −15
  3. 3. f′(2) = 0.7358
  4. 4. f′(2) = 5.482
  5. 5. b = −5
  6. 6. b = −10.5

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