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) = x4 + x2 − 6x − 4. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = x4 + x2 − 6x − 4x = −2
f′(−2) =
2.Easy
xyx = −1

Let f(x) = 4x5 + 8x2 + 9x + 4. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = 4x5 + 8x2 + 9x + 4x = −1
f′(−1) =
3.Medium
xyx = 0.5

Let f(x) = x·sin(x), with x in radians. Find f′(0.5).

f(x) = x·sin(x)x = 0.5 rad
f′(0.5) =
4.Medium
xyx = 1

Let f(x) = ln(x2 + 4). Find f′(1).

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

Let f(x) = x3 + 4.5x2 + 6x − 5. Find the x-coordinate x of the local minimum.

f(x) = x3 + 4.5x2 + 6x − 5
x =
6.Hard
xyx = −1

The tangent line to f(x) = 0.5x2 + 4x + 4 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 + 4x + 4x = −1
b =

Answer key

  1. 1. f′(−2) = −42
  2. 2. f′(−1) = 13
  3. 3. f′(0.5) = 0.9182
  4. 4. f′(1) = 0.4
  5. 5. x = −1
  6. 6. b = 3.5

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