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) = 5x5 − 4x2 − 3x + 5. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = 5x5 − 4x2 − 3x + 5x = −2
f′(−2) =
2.Easy
xyx = 3

Let f(x) = −2x5 + x2 + 6x − 7. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −2x5 + x2 + 6x − 7x = 3
f′(3) =
3.Medium
xyx = 1.5

Let f(x) = x·sin(3x), with x in radians. Find f′(1.5).

f(x) = x·sin(3x)x = 1.5 rad
f′(1.5) =
4.Medium
xyx = 0

Let f(x) = (−2x + 3)4. Find f′(0).

f(x) = (−2x + 3)4x = 0
f′(0) =
5.Hard
xyx = −1

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

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

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

f(x) = 3x2 − 4x − 4x = −2
b =

Answer key

  1. 1. f′(−2) = 413
  2. 2. f′(3) = −798
  3. 3. f′(1.5) = −1.926
  4. 4. f′(0) = −216
  5. 5. b = −5
  6. 6. b = −16

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