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 = −1

Let f(x) = −3x4 + 3x2 − 7x + 2. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −3x4 + 3x2 − 7x + 2x = −1
f′(−1) =
2.Easy
xyx = 3

Let f(x) = −2x3 + 2x2 − 7x − 7. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −2x3 + 2x2 − 7x − 7x = 3
f′(3) =
3.Medium
xyx = 0.5

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

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

Let f(x) = ln(2x2 + 5). Find f′(2).

f(x) = ln(2x2 + 5)x = 2
f′(2) =
5.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 =
6.Hard
xyx = 1

The tangent line to f(x) = 0.5x2 − 4x − 1 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − 4x − 1x = 1
b =

Answer key

  1. 1. f′(−1) = −1
  2. 2. f′(3) = −49
  3. 3. f′(0.5) = 0.9182
  4. 4. f′(2) = 0.6154
  5. 5. b = −7
  6. 6. b = −1.5

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