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) = −3x4 + 6x2 − 6x + 6. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −3x4 + 6x2 − 6x + 6x = 3
f′(3) =
2.Easy
xyx = 2

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

f(x) = 2x4 − 3x2 − 3x + 7x = 2
f′(2) =
3.Medium
xyx = 1.5

Let f(x) = x·sin(x), with x in radians. Find f′(1.5).

f(x) = x·sin(x)x = 1.5 rad
f′(1.5) =
4.Medium
xyx = 3

Let f(x) = ln(2x2 + 5). Find f′(3).

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

The tangent line to f(x) = 3x2 − 5 at x = 2 crosses the y-axis at y = b. Find b.

f(x) = 3x2 − 5x = 2
b =
6.Hard
xy

Let f(x) = x3 − 1.5x2 + 6. Find the x-coordinate x of the local minimum.

f(x) = x3 − 1.5x2 + 6
x =

Answer key

  1. 1. f′(3) = −294
  2. 2. f′(2) = 49
  3. 3. f′(1.5) = 1.104
  4. 4. f′(3) = 0.5217
  5. 5. b = −17
  6. 6. x = 1

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