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) = x5 + 9x2 + 7x − 9. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = x5 + 9x2 + 7x − 9x = −2
f′(−2) =
2.Easy
xyx = 1

Let f(x) = x4 − 7x2 − x − 6. Find the slope of the graph at x = 1, that is f′(1).

f(x) = x4 − 7x2 − x − 6x = 1
f′(1) =
3.Medium
xyx = 3

Let f(x) = ln(3x2 + 2). Find f′(3).

f(x) = ln(3x2 + 2)x = 3
f′(3) =
4.Medium
xyx = 1

Let f(x) = x·sin(2x), with x in radians. Find f′(1).

f(x) = x·sin(2x)x = 1 rad
f′(1) =
5.Hard
xyx = 3

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

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

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

f(x) = 3x2 + 4x − 4x = 3
b =

Answer key

  1. 1. f′(−2) = 51
  2. 2. f′(1) = −11
  3. 3. f′(3) = 0.6207
  4. 4. f′(1) = 0.077
  5. 5. b = 13
  6. 6. b = −31

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