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

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

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

f(x) = 3x5 − 5x2 + 9x − 5x = 2
f′(2) =
3.Medium
xyx = 0.5

Let f(x) = x·e2x. Find f′(0.5).

f(x) = x·e2xx = 0.5
f′(0.5) =
4.Medium
xyx = 2

Let f(x) = (4x − 1)5. Find f′(2).

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

The tangent line to f(x) = 3x2 + 4x + 6 at x = 3 crosses the y-axis at y = b. Find b.

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

The tangent line to f(x) = −x2 − 5x − 1 at x = −2 crosses the y-axis at y = b. Find b.

f(x) = −x2 − 5x − 1x = −2
b =

Answer key

  1. 1. f′(−2) = 375
  2. 2. f′(2) = 229
  3. 3. f′(0.5) = 5.437
  4. 4. f′(2) = 48020
  5. 5. b = −21
  6. 6. b = 3

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