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

f(x) = x3 + 6x2 + 3xx = −3
f′(−3) =
2.Easy
xyx = −1

Let f(x) = x4 + x2 − 7x − 4. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = x4 + x2 − 7x − 4x = −1
f′(−1) =
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

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

f(x) = x·sin(x)x = 1 rad
f′(1) =
5.Hard
xy

Let f(x) = x3 + 4.5x2 − 1. Find the x-coordinate x of the local maximum.

f(x) = x3 + 4.5x2 − 1
x =
6.Hard
xy

Let f(x) = x3 − 12x2 + 45x + 5. Find the x-coordinate x of the local maximum.

f(x) = x3 − 12x2 + 45x + 5
x =

Answer key

  1. 1. f′(−3) = −6
  2. 2. f′(−1) = −13
  3. 3. f′(1) = 5488
  4. 4. f′(1) = 1.382
  5. 5. x = −3
  6. 6. x = 3

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