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) = −5x4 − 3x2 − 3x − 6. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −5x4 − 3x2 − 3x − 6x = 3
f′(3) =
2.Easy
xyx = 3

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

f(x) = x5 − 6x2 + 3xx = 3
f′(3) =
3.Medium
xyx = 3

Let f(x) = ln(2x2 + 4). Find f′(3).

f(x) = ln(2x2 + 4)x = 3
f′(3) =
4.Medium
xyx = 1.5

Let f(x) = x2·e−0.5x. Find f′(1.5).

f(x) = x2·e−0.5xx = 1.5
f′(1.5) =
5.Hard
xy

Let f(x) = x3 + 7.5x2 + 12x + 2. Find the x-coordinate x of the local maximum.

f(x) = x3 + 7.5x2 + 12x + 2
x =
6.Hard
xyx = 3

The tangent line to f(x) = x2 + x + 6 at x = 3 crosses the y-axis at y = b. Find b.

f(x) = x2 + x + 6x = 3
b =

Answer key

  1. 1. f′(3) = −561
  2. 2. f′(3) = 372
  3. 3. f′(3) = 0.5455
  4. 4. f′(1.5) = 0.8857
  5. 5. x = −4
  6. 6. b = −3

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