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 = −1

Let f(x) = x5 + 4x2 − 8x − 8. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = x5 + 4x2 − 8x − 8x = −1
f′(−1) =
2.Easy
xyx = 2

Let f(x) = 5x5 − 2x2 + 8x + 1. Find the slope of the graph at x = 2, that is f′(2).

f(x) = 5x5 − 2x2 + 8x + 1x = 2
f′(2) =
3.Medium
xyx = −2

Let f(x) = ln(3x2 + 5). Find f′(−2).

f(x) = ln(3x2 + 5)x = −2
f′(−2) =
4.Medium
xyx = −2

Let f(x) = ln(x2 + 2). Find f′(−2).

f(x) = ln(x2 + 2)x = −2
f′(−2) =
5.Hard
xyx = 3

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

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

The tangent line to f(x) = 2x2 + x − 4 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = 2x2 + x − 4x = −1
b =

Answer key

  1. 1. f′(−1) = −11
  2. 2. f′(2) = 400
  3. 3. f′(−2) = −0.7059
  4. 4. f′(−2) = −0.6667
  5. 5. b = 12
  6. 6. b = −6

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