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

f(x) = x5 + 5x2 − 4x + 4x = 1
f′(1) =
2.Easy
xyx = −1

Let f(x) = 5x3 + 8x2 + 3x + 8. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 5x3 + 8x2 + 3x + 8x = −1
f′(−1) =
3.Medium
xyx = 2

Let f(x) = (3x − 3)5. Find f′(2).

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

Let f(x) = ln(2x2 + 5). Find f′(3).

f(x) = ln(2x2 + 5)x = 3
f′(3) =
5.Hard
xyx = 1

The tangent line to f(x) = 2x2 − 5x − 3 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 2x2 − 5x − 3x = 1
b =
6.Hard
xyx = −2

The tangent line to f(x) = x2 − 3x − 5 at x = −2 crosses the y-axis at y = b. Find b.

f(x) = x2 − 3x − 5x = −2
b =

Answer key

  1. 1. f′(1) = 11
  2. 2. f′(−1) = 2
  3. 3. f′(2) = 1215
  4. 4. f′(3) = 0.5217
  5. 5. b = −5
  6. 6. b = −9

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