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) = −4x5 + x2 + 3x + 2. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −4x5 + x2 + 3x + 2x = −3
f′(−3) =
2.Easy
xyx = 1

Let f(x) = −4x4 − 7x2 + 4x + 9. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −4x4 − 7x2 + 4x + 9x = 1
f′(1) =
3.Medium
xyx = 3

Let f(x) = ln(3x2 + 1). Find f′(3).

f(x) = ln(3x2 + 1)x = 3
f′(3) =
4.Medium
xyx = 1.5

Let f(x) = x3·e0.5x. Find f′(1.5).

f(x) = x3·e0.5xx = 1.5
f′(1.5) =
5.Hard
xyx = −2

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

f(x) = 0.5x2 + 2x − 5x = −2
b =
6.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 =

Answer key

  1. 1. f′(−3) = −1623
  2. 2. f′(1) = −26
  3. 3. f′(3) = 0.6429
  4. 4. f′(1.5) = 17.86
  5. 5. b = −7
  6. 6. x = −4

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