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) = −4x5 − 6x2 + 9x + 2. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −4x5 − 6x2 + 9x + 2x = −3
f′(−3) =
2.Easy
xyx = 2

Let f(x) = x5 − 7x2 + 6x + 2. Find the slope of the graph at x = 2, that is f′(2).

f(x) = x5 − 7x2 + 6x + 2x = 2
f′(2) =
3.Medium
xyx = 1.5

Let f(x) = x·sin(3x), with x in radians. Find f′(1.5).

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

Let f(x) = ln(3x2 + 1). Find f′(3).

f(x) = ln(3x2 + 1)x = 3
f′(3) =
5.Hard
xyx = 2

The tangent line to f(x) = 0.5x2 + 3x − 5 at x = 2 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 + 3x − 5x = 2
b =
6.Hard
xy

Let f(x) = x3 − 7.5x2 + 12x + 1. Find the x-coordinate x of the local minimum.

f(x) = x3 − 7.5x2 + 12x + 1
x =

Answer key

  1. 1. f′(−3) = −1575
  2. 2. f′(2) = 58
  3. 3. f′(1.5) = −1.926
  4. 4. f′(3) = 0.6429
  5. 5. b = −7
  6. 6. x = 4

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