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) = 3x3 − 5x2 − 7x − 6. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = 3x3 − 5x2 − 7x − 6x = −2
f′(−2) =
2.Easy
xyx = 1

Let f(x) = 5x4 − 3x2 − 2x − 4. Find the slope of the graph at x = 1, that is f′(1).

f(x) = 5x4 − 3x2 − 2x − 4x = 1
f′(1) =
3.Medium
xyx = 2

Let f(x) = x3·ex. Find f′(2).

f(x) = x3·exx = 2
f′(2) =
4.Medium
xyx = 1.5

Let f(x) = x2·ex. Find f′(1.5).

f(x) = x2·exx = 1.5
f′(1.5) =
5.Hard
xyx = 1

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

f(x) = −x2 − 3x + 3x = 1
b =
6.Hard
xyx = −1

The tangent line to f(x) = x2 − x + 5 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = x2 − x + 5x = −1
b =

Answer key

  1. 1. f′(−2) = 49
  2. 2. f′(1) = 12
  3. 3. f′(2) = 147.8
  4. 4. f′(1.5) = 23.53
  5. 5. b = 4
  6. 6. b = 4

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