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 = −1

Let f(x) = 2x4 + 4x2 + x − 4. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 2x4 + 4x2 + x − 4x = −1
f′(−1) =
2.Easy
xyx = 3

Let f(x) = −5x4 + 9x2 + 4. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −5x4 + 9x2 + 4x = 3
f′(3) =
3.Medium
xyx = 1

Let f(x) = ln(2x2 + 1). Find f′(1).

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

Let f(x) = x3·ex. Find f′(2).

f(x) = x3·exx = 2
f′(2) =
5.Hard
xy

Let f(x) = x3 − 3x. Find the x-coordinate x of the local minimum.

f(x) = x3 − 3x
x =
6.Hard
xyx = 2

The tangent line to f(x) = −x2 − 5x − 6 at x = 2 crosses the y-axis at y = b. Find b.

f(x) = −x2 − 5x − 6x = 2
b =

Answer key

  1. 1. f′(−1) = −15
  2. 2. f′(3) = −486
  3. 3. f′(1) = 1.333
  4. 4. f′(2) = 147.8
  5. 5. x = 1
  6. 6. b = −2

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