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) = −2x3 + 7x2 − 4x + 8. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −2x3 + 7x2 − 4x + 8x = −2
f′(−2) =
2.Easy
xyx = −2

Let f(x) = −x4 + x2 + 5x − 9. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −x4 + x2 + 5x − 9x = −2
f′(−2) =
3.Medium
xyx = 2

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

f(x) = x·sin(2x)x = 2 rad
f′(2) =
4.Medium
xyx = 1

Let f(x) = (−2x + 5)4. Find f′(1).

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

The tangent line to f(x) = 3x2 + x + 2 at x = 1 crosses the y-axis at y = b. Find b.

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

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

f(x) = 3x2 − 4x + 4x = −1
b =

Answer key

  1. 1. f′(−2) = −56
  2. 2. f′(−2) = 33
  3. 3. f′(2) = −3.371
  4. 4. f′(1) = −216
  5. 5. b = −1
  6. 6. b = 1

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