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) = −4x4 − 2x2 + x + 2. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −4x4 − 2x2 + x + 2x = −1
f′(−1) =
2.Easy
xyx = −3

Let f(x) = −2x3 − 4x2 − 4x + 6. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −2x3 − 4x2 − 4x + 6x = −3
f′(−3) =
3.Medium
xyx = 0.5

Let f(x) = x·sin(2x), with x in radians. Find f′(0.5).

f(x) = x·sin(2x)x = 0.5 rad
f′(0.5) =
4.Medium
xyx = 1.5

Let f(x) = x2·e0.5x. Find f′(1.5).

f(x) = x2·e0.5xx = 1.5
f′(1.5) =
5.Hard
xyx = −1

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

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

The tangent line to f(x) = 0.5x2 + 2x − 6 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 + 2x − 6x = 1
b =

Answer key

  1. 1. f′(−1) = 21
  2. 2. f′(−3) = −34
  3. 3. f′(0.5) = 1.382
  4. 4. f′(1.5) = 8.733
  5. 5. b = −7
  6. 6. b = −6.5

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