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

f(x) = 2x3 + 7x2 + 7xx = −2
f′(−2) =
2.Easy
xyx = 3

Let f(x) = 5x3 + 6x2 + 8x + 3. Find the slope of the graph at x = 3, that is f′(3).

f(x) = 5x3 + 6x2 + 8x + 3x = 3
f′(3) =
3.Medium
xyx = 1

Let f(x) = ln(3x2 + 1). Find f′(1).

f(x) = ln(3x2 + 1)x = 1
f′(1) =
4.Medium
xyx = 0.5

Let f(x) = x·e0.5x. Find f′(0.5).

f(x) = x·e0.5xx = 0.5
f′(0.5) =
5.Hard
xyx = 1

The tangent line to f(x) = x2 + 4x − 4 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = x2 + 4x − 4x = 1
b =
6.Hard
xy

Let f(x) = x3 + 9x2 + 24x + 3. Find the x-coordinate x of the local maximum.

f(x) = x3 + 9x2 + 24x + 3
x =

Answer key

  1. 1. f′(−2) = 3
  2. 2. f′(3) = 179
  3. 3. f′(1) = 1.5
  4. 4. f′(0.5) = 1.605
  5. 5. b = −5
  6. 6. x = −4

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