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) = 2x5 − 8x2 + 9x − 4. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 2x5 − 8x2 + 9x − 4x = −1
f′(−1) =
2.Easy
xyx = −2

Let f(x) = −5x4 − 7x2 + 6x + 2. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −5x4 − 7x2 + 6x + 2x = −2
f′(−2) =
3.Medium
xyx = 0.5

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

f(x) = x·sin(x)x = 0.5 rad
f′(0.5) =
4.Medium
xyx = 1

Let f(x) = (3x + 3)4. Find f′(1).

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

Let f(x) = x3 − 9x2 + 15x. Find the x-coordinate x of the local maximum.

f(x) = x3 − 9x2 + 15x
x =
6.Hard
xyx = 2

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

f(x) = 2x2 − 4x + 4x = 2
b =

Answer key

  1. 1. f′(−1) = 35
  2. 2. f′(−2) = 194
  3. 3. f′(0.5) = 0.9182
  4. 4. f′(1) = 2592
  5. 5. x = 1
  6. 6. b = −4

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