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) = −5x5 + 2x2 + 3x − 2. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −5x5 + 2x2 + 3x − 2x = 2
f′(2) =
2.Easy
xyx = 2

Let f(x) = −5x5 + 8x2 − 8x + 2. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −5x5 + 8x2 − 8x + 2x = 2
f′(2) =
3.Medium
xyx = 0.5

Let f(x) = x·sin(2x), with x in radians. Find f′(0.5).

f(x) = x·sin(2x)x = 0.5 rad
f′(0.5) =
4.Medium
xyx = 1.5

Let f(x) = x3·e2x. Find f′(1.5).

f(x) = x3·e2xx = 1.5
f′(1.5) =
5.Hard
xy

Let f(x) = x3 − 13.5x2 + 54x + 4. Find the x-coordinate x of the local minimum.

f(x) = x3 − 13.5x2 + 54x + 4
x =
6.Hard
xyx = 1

The tangent line to f(x) = x2 − 5x + 6 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = x2 − 5x + 6x = 1
b =

Answer key

  1. 1. f′(2) = −389
  2. 2. f′(2) = −376
  3. 3. f′(0.5) = 1.382
  4. 4. f′(1.5) = 271.2
  5. 5. x = 6
  6. 6. b = 5

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