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) = 5x3 − 4x2 + 6x − 3. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = 5x3 − 4x2 + 6x − 3x = −3
f′(−3) =
2.Easy
xyx = 1

Let f(x) = 3x3 − 7x2 − 9x − 8. Find the slope of the graph at x = 1, that is f′(1).

f(x) = 3x3 − 7x2 − 9x − 8x = 1
f′(1) =
3.Medium
xyx = 1.5

Let f(x) = x·ex. Find f′(1.5).

f(x) = x·exx = 1.5
f′(1.5) =
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
xy

Let f(x) = x3 + 7.5x2 + 12x − 1. Find the x-coordinate x of the local minimum.

f(x) = x3 + 7.5x2 + 12x − 1
x =
6.Hard
xyx = 1

The tangent line to f(x) = x2 − 3 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = x2 − 3x = 1
b =

Answer key

  1. 1. f′(−3) = 165
  2. 2. f′(1) = −14
  3. 3. f′(1.5) = 11.2
  4. 4. f′(1.5) = 2.391
  5. 5. x = −1
  6. 6. b = −4

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