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) = −x5 + 4x2 − x + 4. Find the slope of the graph at x = 1, that is f′(1).

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

Let f(x) = 4x5 − 6x2 − 7x + 2. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = 4x5 − 6x2 − 7x + 2x = −3
f′(−3) =
3.Medium
xyx = 1

Let f(x) = ln(x2 + 5). Find f′(1).

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

Let f(x) = x2·e2x. Find f′(1).

f(x) = x2·e2xx = 1
f′(1) =
5.Hard
xy

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

f(x) = x3 − 4.5x2 − 2
x =
6.Hard
xyx = −1

The tangent line to f(x) = 2x2 + 3x − 4 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = 2x2 + 3x − 4x = −1
b =

Answer key

  1. 1. f′(1) = 2
  2. 2. f′(−3) = 1649
  3. 3. f′(1) = 0.3333
  4. 4. f′(1) = 29.56
  5. 5. x = 3
  6. 6. b = −6

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