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) = −5x3 − 5x2 + 4x + 1. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −5x3 − 5x2 + 4x + 1x = 1
f′(1) =
2.Easy
xyx = −2

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

f(x) = 2x3 + 6x2 − x + 3x = −2
f′(−2) =
3.Medium
xyx = 1

Let f(x) = x·sin(2x), with x in radians. Find f′(1).

f(x) = x·sin(2x)x = 1 rad
f′(1) =
4.Medium
xyx = 1

Let f(x) = (4x + 3)3. Find f′(1).

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

The tangent line to f(x) = 2x2 − 2x − 4 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 2x2 − 2x − 4x = 1
b =
6.Hard
xyx = −2

The tangent line to f(x) = x2 − 4x − 1 at x = −2 crosses the y-axis at y = b. Find b.

f(x) = x2 − 4x − 1x = −2
b =

Answer key

  1. 1. f′(1) = −21
  2. 2. f′(−2) = −1
  3. 3. f′(1) = 0.077
  4. 4. f′(1) = 588
  5. 5. b = −6
  6. 6. b = −5

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