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) = 3x3 + 6x2 + 5x + 6. Find the slope of the graph at x = 2, that is f′(2).

f(x) = 3x3 + 6x2 + 5x + 6x = 2
f′(2) =
2.Easy
xyx = −2

Let f(x) = −x4 − 2x2 − 6x + 5. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −x4 − 2x2 − 6x + 5x = −2
f′(−2) =
3.Medium
xyx = 2

Let f(x) = (2x + 3)3. Find f′(2).

f(x) = (2x + 3)3x = 2
f′(2) =
4.Medium
xyx = 1

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

f(x) = x·sin(x)x = 1 rad
f′(1) =
5.Hard
xyx = −2

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

f(x) = 3x2 − 4x − 3x = −2
b =
6.Hard
xy

Let f(x) = x3 − 12x. Find the x-coordinate x of the local maximum.

f(x) = x3 − 12x
x =

Answer key

  1. 1. f′(2) = 65
  2. 2. f′(−2) = 34
  3. 3. f′(2) = 294
  4. 4. f′(1) = 1.382
  5. 5. b = −15
  6. 6. x = −2

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