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) = x4 + 6x2 − 6x + 7. Find the slope of the graph at x = 3, that is f′(3).

f(x) = x4 + 6x2 − 6x + 7x = 3
f′(3) =
2.Easy
xyx = −3

Let f(x) = x5 − 4x2 − 5x + 4. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = x5 − 4x2 − 5x + 4x = −3
f′(−3) =
3.Medium
xyx = −1

Let f(x) = (3x + 1)5. Find f′(−1).

f(x) = (3x + 1)5x = −1
f′(−1) =
4.Medium
xyx = 1

Let f(x) = x·sin(3x), with x in radians. Find f′(1).

f(x) = x·sin(3x)x = 1 rad
f′(1) =
5.Hard
xyx = −2

The tangent line to f(x) = 0.5x2 + x − 5 at x = −2 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 + x − 5x = −2
b =
6.Hard
xy

Let f(x) = x3 − 9x2 + 15x − 3. Find the x-coordinate x of the local minimum.

f(x) = x3 − 9x2 + 15x − 3
x =

Answer key

  1. 1. f′(3) = 138
  2. 2. f′(−3) = 424
  3. 3. f′(−1) = 240
  4. 4. f′(1) = −2.829
  5. 5. b = −7
  6. 6. x = 5

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