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) = x3 + 8x2 − x + 3. Find the slope of the graph at x = 1, that is f′(1).

f(x) = x3 + 8x2 − x + 3x = 1
f′(1) =
2.Easy
xyx = 3

Let f(x) = −2x3 − x2 + 6x − 7. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −2x3 − x2 + 6x − 7x = 3
f′(3) =
3.Medium
xyx = 1

Let f(x) = x3·e2x. Find f′(1).

f(x) = x3·e2xx = 1
f′(1) =
4.Medium
xyx = 1

Let f(x) = x·sin(3x), with x in radians. Find f′(1).

f(x) = x·sin(3x)x = 1 rad
f′(1) =
5.Hard
xyx = 3

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

f(x) = −x2 + x + 4x = 3
b =
6.Hard
xyx = 1

The tangent line to f(x) = 0.5x2 + 5x + 4 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 + 5x + 4x = 1
b =

Answer key

  1. 1. f′(1) = 18
  2. 2. f′(3) = −54
  3. 3. f′(1) = 36.95
  4. 4. f′(1) = −2.829
  5. 5. b = 13
  6. 6. b = 3.5

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