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

f(x) = 4x5 − 3x2 + 7x + 2x = 3
f′(3) =
2.Easy
xyx = 1

Let f(x) = 3x5 + 8x2 − 3x − 7. Find the slope of the graph at x = 1, that is f′(1).

f(x) = 3x5 + 8x2 − 3x − 7x = 1
f′(1) =
3.Medium
xyx = 2

Let f(x) = x·ex. Find f′(2).

f(x) = x·exx = 2
f′(2) =
4.Medium
xyx = 3

Let f(x) = ln(x2 + 5). Find f′(3).

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

Let f(x) = x3 − 10.5x2 + 36x + 5. Find the x-coordinate x of the local minimum.

f(x) = x3 − 10.5x2 + 36x + 5
x =
6.Hard
xy

Let f(x) = x3 − 12x2 + 36x + 6. Find the x-coordinate x of the local minimum.

f(x) = x3 − 12x2 + 36x + 6
x =

Answer key

  1. 1. f′(3) = 1609
  2. 2. f′(1) = 28
  3. 3. f′(2) = 22.17
  4. 4. f′(3) = 0.4286
  5. 5. x = 4
  6. 6. x = 6

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