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 + 2. Find the slope of the graph at x = 2, that is f′(2).

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

Let f(x) = −5x4 + 2x2 − 8x − 7. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −5x4 + 2x2 − 8x − 7x = 2
f′(2) =
3.Medium
xyx = 1.5

Let f(x) = x·ex. Find f′(1.5).

f(x) = x·exx = 1.5
f′(1.5) =
4.Medium
xyx = 1.5

Let f(x) = x·sin(3x), with x in radians. Find f′(1.5).

f(x) = x·sin(3x)x = 1.5 rad
f′(1.5) =
5.Hard
xy

Let f(x) = x3 − 1.5x2. Find the x-coordinate x of the local minimum.

f(x) = x3 − 1.5x2
x =
6.Hard
xyx = −1

The tangent line to f(x) = 3x2 − 6 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = 3x2 − 6x = −1
b =

Answer key

  1. 1. f′(2) = −72
  2. 2. f′(2) = −160
  3. 3. f′(1.5) = 11.2
  4. 4. f′(1.5) = −1.926
  5. 5. x = 1
  6. 6. b = −9

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