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

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

Let f(x) = −x5 + 6x2 + 9x − 2. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −x5 + 6x2 + 9x − 2x = 1
f′(1) =
3.Medium
xyx = −1

Let f(x) = (4x + 5)5. Find f′(−1).

f(x) = (4x + 5)5x = −1
f′(−1) =
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) = −x2 − 3x − 3 at x = 2 crosses the y-axis at y = b. Find b.

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

Let f(x) = x3 + 1.5x2 − 6x + 6. Find the x-coordinate x of the local minimum.

f(x) = x3 + 1.5x2 − 6x + 6
x =

Answer key

  1. 1. f′(2) = −313
  2. 2. f′(1) = 16
  3. 3. f′(−1) = 20
  4. 4. f′(1) = 1.382
  5. 5. b = 1
  6. 6. x = 1

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