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

f(x) = x5 − 7x2 − 8x − 9x = −1
f′(−1) =
2.Easy
xyx = 3

Let f(x) = −5x5 − 3x2 − x − 1. Find the slope of the graph at x = 3, that is f′(3).

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

Let f(x) = ln(2x2 + 1). Find f′(1).

f(x) = ln(2x2 + 1)x = 1
f′(1) =
4.Medium
xyx = 0.5

Let f(x) = x·sin(3x), with x in radians. Find f′(0.5).

f(x) = x·sin(3x)x = 0.5 rad
f′(0.5) =
5.Hard
xyx = −1

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

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

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

f(x) = 3x2 − 3x + 4x = 3
b =

Answer key

  1. 1. f′(−1) = 11
  2. 2. f′(3) = −2044
  3. 3. f′(1) = 1.333
  4. 4. f′(0.5) = 1.104
  5. 5. b = 1
  6. 6. b = −23

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