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) = 3x3 − 7x2 + x − 9. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = 3x3 − 7x2 + x − 9x = −3
f′(−3) =
2.Easy
xyx = −2

Let f(x) = 5x5 + 2x2 + 9x + 9. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = 5x5 + 2x2 + 9x + 9x = −2
f′(−2) =
3.Medium
xyx = 3

Let f(x) = ln(3x2 + 2). Find f′(3).

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

Let f(x) = ln(2x2 + 4). Find f′(3).

f(x) = ln(2x2 + 4)x = 3
f′(3) =
5.Hard
xyx = 3

The tangent line to f(x) = 3x2 − 5x + 6 at x = 3 crosses the y-axis at y = b. Find b.

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

Let f(x) = x3 − 4.5x2 + 6x − 2. Find the x-coordinate x of the local maximum.

f(x) = x3 − 4.5x2 + 6x − 2
x =

Answer key

  1. 1. f′(−3) = 124
  2. 2. f′(−2) = 401
  3. 3. f′(3) = 0.6207
  4. 4. f′(3) = 0.5455
  5. 5. b = −21
  6. 6. x = 1

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