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) = 5x5 + 7x2 + 4x + 1. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = 5x5 + 7x2 + 4x + 1x = −3
f′(−3) =
2.Easy
xyx = −1

Let f(x) = −4x5 − 5x2 − 7x − 5. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −4x5 − 5x2 − 7x − 5x = −1
f′(−1) =
3.Medium
xyx = 1

Let f(x) = (4x + 1)5. Find f′(1).

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

Let f(x) = ln(x2 + 4). Find f′(−1).

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

The tangent line to f(x) = x2 − 5 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = x2 − 5x = −1
b =
6.Hard
xy

Let f(x) = x3 − 4.5x2 + 6x − 3. Find the x-coordinate x of the local minimum.

f(x) = x3 − 4.5x2 + 6x − 3
x =

Answer key

  1. 1. f′(−3) = 1987
  2. 2. f′(−1) = −17
  3. 3. f′(1) = 12500
  4. 4. f′(−1) = −0.4
  5. 5. b = −6
  6. 6. x = 2

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