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) = 5x5 − x2 − 2x − 7. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = 5x5 − x2 − 2x − 7x = −3
f′(−3) =
2.Easy
xyx = −3

Let f(x) = −2x5 − 5x2 + 9x − 8. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −2x5 − 5x2 + 9x − 8x = −3
f′(−3) =
3.Medium
xyx = 1

Let f(x) = x3·e0.5x. Find f′(1).

f(x) = x3·e0.5xx = 1
f′(1) =
4.Medium
xyx = 2

Let f(x) = ln(3x2 + 4). Find f′(2).

f(x) = ln(3x2 + 4)x = 2
f′(2) =
5.Hard
xyx = −1

The tangent line to f(x) = 3x2 − 5x + 4 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = 3x2 − 5x + 4x = −1
b =
6.Hard
xyx = 2

The tangent line to f(x) = 2x2 − 4x − 5 at x = 2 crosses the y-axis at y = b. Find b.

f(x) = 2x2 − 4x − 5x = 2
b =

Answer key

  1. 1. f′(−3) = 2029
  2. 2. f′(−3) = −771
  3. 3. f′(1) = 5.771
  4. 4. f′(2) = 0.75
  5. 5. b = 1
  6. 6. b = −13

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