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

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

Let f(x) = −x4 + 6x2 + 4x − 9. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −x4 + 6x2 + 4x − 9x = 2
f′(2) =
3.Medium
xyx = −1

Let f(x) = ln(2x2 + 5). Find f′(−1).

f(x) = ln(2x2 + 5)x = −1
f′(−1) =
4.Medium
xyx = 0

Let f(x) = (−2x − 3)4. Find f′(0).

f(x) = (−2x − 3)4x = 0
f′(0) =
5.Hard
xyx = −2

The tangent line to f(x) = 2x2 − 4x − 3 at x = −2 crosses the y-axis at y = b. Find b.

f(x) = 2x2 − 4x − 3x = −2
b =
6.Hard
xyx = −1

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

f(x) = 2x2 − 4x − 4x = −1
b =

Answer key

  1. 1. f′(1) = 22
  2. 2. f′(2) = −4
  3. 3. f′(−1) = −0.5714
  4. 4. f′(0) = 216
  5. 5. b = −11
  6. 6. b = −6

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