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) = −5x5 − 3x2 − 5x + 1. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −5x5 − 3x2 − 5x + 1x = 3
f′(3) =
2.Easy
xyx = −2

Let f(x) = 5x3 + 5x2 + 7x − 5. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = 5x3 + 5x2 + 7x − 5x = −2
f′(−2) =
3.Medium
xyx = 2

Let f(x) = ln(3x2 + 4). Find f′(2).

f(x) = ln(3x2 + 4)x = 2
f′(2) =
4.Medium
xyx = 1.5

Let f(x) = x·e−0.5x. Find f′(1.5).

f(x) = x·e−0.5xx = 1.5
f′(1.5) =
5.Hard
xyx = 1

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

f(x) = x2 − 2x = 1
b =
6.Hard
xy

Let f(x) = x3 − 10.5x2 + 30x + 3. Find the x-coordinate x of the local maximum.

f(x) = x3 − 10.5x2 + 30x + 3
x =

Answer key

  1. 1. f′(3) = −2048
  2. 2. f′(−2) = 47
  3. 3. f′(2) = 0.75
  4. 4. f′(1.5) = 0.1181
  5. 5. b = −3
  6. 6. x = 2

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