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 = −3

Let f(x) = 3x5 − 5x2 − 9x − 2. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = 3x5 − 5x2 − 9x − 2x = −3
f′(−3) =
2.Easy
xyx = 3

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

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

Let f(x) = x·sin(3x), with x in radians. Find f′(2).

f(x) = x·sin(3x)x = 2 rad
f′(2) =
4.Medium
xyx = 2

Let f(x) = (3x − 3)4. Find f′(2).

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

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

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

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

f(x) = 2x2 + x − 5x = 1
b =

Answer key

  1. 1. f′(−3) = 1236
  2. 2. f′(3) = −1995
  3. 3. f′(2) = 5.482
  4. 4. f′(2) = 324
  5. 5. b = −3
  6. 6. b = −7

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