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 = −2

Let f(x) = −4x5 + 8x2 − 5. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −4x5 + 8x2 − 5x = −2
f′(−2) =
2.Easy
xyx = 1

Let f(x) = −4x4 + 3x2 − x − 6. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −4x4 + 3x2 − x − 6x = 1
f′(1) =
3.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) =
4.Medium
xyx = 2

Let f(x) = x2·ex. Find f′(2).

f(x) = x2·exx = 2
f′(2) =
5.Hard
xy

Let f(x) = x3 − 9x2 + 24x + 1. Find the x-coordinate x of the local maximum.

f(x) = x3 − 9x2 + 24x + 1
x =
6.Hard
xyx = 1

The tangent line to f(x) = 3x2 − 3x + 2 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 3x2 − 3x + 2x = 1
b =

Answer key

  1. 1. f′(−2) = −352
  2. 2. f′(1) = −11
  3. 3. f′(2) = 5.482
  4. 4. f′(2) = 59.11
  5. 5. x = 2
  6. 6. b = −1

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