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 = 2

Let f(x) = 3x3 − 7x2 + 4x − 2. Find the slope of the graph at x = 2, that is f′(2).

f(x) = 3x3 − 7x2 + 4x − 2x = 2
f′(2) =
2.Easy
xyx = −1

Let f(x) = −5x3 + x2 − x + 6. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −5x3 + x2 − x + 6x = −1
f′(−1) =
3.Medium
xyx = −2

Let f(x) = ln(x2 + 5). Find f′(−2).

f(x) = ln(x2 + 5)x = −2
f′(−2) =
4.Medium
xyx = 1

Let f(x) = (3x + 1)3. Find f′(1).

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

The tangent line to f(x) = 0.5x2 + x + 6 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 + x + 6x = 1
b =
6.Hard
xy

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

f(x) = x3 + 6x2 − 2
x =

Answer key

  1. 1. f′(2) = 12
  2. 2. f′(−1) = −18
  3. 3. f′(−2) = −0.4444
  4. 4. f′(1) = 144
  5. 5. b = 5.5
  6. 6. x = −4

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