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 − 8x2 − 7x + 9. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 4x4 − 8x2 − 7x + 9x = −1
f′(−1) =
2.Easy
xyx = −2

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

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

Let f(x) = (4x − 3)4. Find f′(1).

f(x) = (4x − 3)4x = 1
f′(1) =
4.Medium
xyx = 1.5

Let f(x) = x·sin(3x), with x in radians. Find f′(1.5).

f(x) = x·sin(3x)x = 1.5 rad
f′(1.5) =
5.Hard
xyx = 3

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

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

The tangent line to f(x) = x2 − 4x − 6 at x = 3 crosses the y-axis at y = b. Find b.

f(x) = x2 − 4x − 6x = 3
b =

Answer key

  1. 1. f′(−1) = −7
  2. 2. f′(−2) = −142
  3. 3. f′(1) = 16
  4. 4. f′(1.5) = −1.926
  5. 5. b = −10
  6. 6. b = −15

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