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) = 2x4 + 2x2 − 8x − 4. Find the slope of the graph at x = 2, that is f′(2).

f(x) = 2x4 + 2x2 − 8x − 4x = 2
f′(2) =
2.Easy
xyx = 2

Let f(x) = −4x5 + 7x2 − 7x + 1. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −4x5 + 7x2 − 7x + 1x = 2
f′(2) =
3.Medium
xyx = 2

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

f(x) = x·sin(2x)x = 2 rad
f′(2) =
4.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) =
5.Hard
xyx = −2

The tangent line to f(x) = 0.5x2 − 2x at x = −2 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − 2xx = −2
b =
6.Hard
xyx = −2

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

f(x) = 2x2 − 3x + 2x = −2
b =

Answer key

  1. 1. f′(2) = 64
  2. 2. f′(2) = −299
  3. 3. f′(2) = −3.371
  4. 4. f′(2) = 5.482
  5. 5. b = −2
  6. 6. b = −6

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