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 + 8x2 − 6x + 1. Find the slope of the graph at x = 1, that is f′(1).

f(x) = x5 + 8x2 − 6x + 1x = 1
f′(1) =
2.Easy
xyx = −2

Let f(x) = −4x5 − 9x2. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −4x5 − 9x2x = −2
f′(−2) =
3.Medium
xyx = 2

Let f(x) = x·ex. Find f′(2).

f(x) = x·exx = 2
f′(2) =
4.Medium
xyx = 2

Let f(x) = x2·e−0.5x. Find f′(2).

f(x) = x2·e−0.5xx = 2
f′(2) =
5.Hard
xy

Let f(x) = x3 − 15x2 + 63x + 3. Find the x-coordinate x of the local maximum.

f(x) = x3 − 15x2 + 63x + 3
x =
6.Hard
xyx = −1

The tangent line to f(x) = 3x2 + 3x + 6 at x = −1 crosses the y-axis at y = b. Find b.

f(x) = 3x2 + 3x + 6x = −1
b =

Answer key

  1. 1. f′(1) = 15
  2. 2. f′(−2) = −284
  3. 3. f′(2) = 22.17
  4. 4. f′(2) = 0.7358
  5. 5. x = 3
  6. 6. b = 3

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