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 = 3

Let f(x) = −x3 + x2 − 9x + 7. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −x3 + x2 − 9x + 7x = 3
f′(3) =
2.Easy
xyx = 2

Let f(x) = 4x5 + 7x2 − 3x + 4. Find the slope of the graph at x = 2, that is f′(2).

f(x) = 4x5 + 7x2 − 3x + 4x = 2
f′(2) =
3.Medium
xyx = 0.5

Let f(x) = x·e0.5x. Find f′(0.5).

f(x) = x·e0.5xx = 0.5
f′(0.5) =
4.Medium
xyx = 0.5

Let f(x) = x·sin(3x), with x in radians. Find f′(0.5).

f(x) = x·sin(3x)x = 0.5 rad
f′(0.5) =
5.Hard
xyx = −1

The tangent line to f(x) = 0.5x2 + 3x + 3 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 + 3x + 3x = −1
b =
6.Hard
xyx = −1

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

f(x) = −x2 − 3x − 3x = −1
b =

Answer key

  1. 1. f′(3) = −30
  2. 2. f′(2) = 345
  3. 3. f′(0.5) = 1.605
  4. 4. f′(0.5) = 1.104
  5. 5. b = 2.5
  6. 6. b = −2

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