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 − 8x2 + 5x. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −x4 − 8x2 + 5xx = −3
f′(−3) =
2.Easy
xyx = 3

Let f(x) = 4x3 + 9x2 + 3x − 4. Find the slope of the graph at x = 3, that is f′(3).

f(x) = 4x3 + 9x2 + 3x − 4x = 3
f′(3) =
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) = x3·e−0.5x. Find f′(1.5).

f(x) = x3·e−0.5xx = 1.5
f′(1.5) =
5.Hard
xyx = −2

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

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

The tangent line to f(x) = 0.5x2 − 5x − 6 at x = 2 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − 5x − 6x = 2
b =

Answer key

  1. 1. f′(−3) = 161
  2. 2. f′(3) = 165
  3. 3. f′(2) = 0.75
  4. 4. f′(1.5) = 2.391
  5. 5. b = −3
  6. 6. b = −8

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