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) = x3 + 2x2 + 7x − 5. Find the slope of the graph at x = 3, that is f′(3).

f(x) = x3 + 2x2 + 7x − 5x = 3
f′(3) =
2.Easy
xyx = −1

Let f(x) = −5x4 − 3x2 + 4x + 5. Find the slope of the graph at x = −1, that is f′(−1).

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

Let f(x) = (2x − 1)5. Find f′(−1).

f(x) = (2x − 1)5x = −1
f′(−1) =
4.Medium
xyx = 1.5

Let f(x) = x·sin(3x), with x in radians. Find f′(1.5).

f(x) = x·sin(3x)x = 1.5 rad
f′(1.5) =
5.Hard
xy

Let f(x) = x3 − 12x2 + 45x − 4. Find the x-coordinate x of the local maximum.

f(x) = x3 − 12x2 + 45x − 4
x =
6.Hard
xyx = 1

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

f(x) = x2 + 4x − 4x = 1
b =

Answer key

  1. 1. f′(3) = 46
  2. 2. f′(−1) = 30
  3. 3. f′(−1) = 810
  4. 4. f′(1.5) = −1.926
  5. 5. x = 3
  6. 6. b = −5

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