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) = −x4 − 6x2 − 5x + 9. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −x4 − 6x2 − 5x + 9x = 1
f′(1) =
2.Easy
xyx = 1

Let f(x) = −3x5 − x2 + 2x − 7. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −3x5 − x2 + 2x − 7x = 1
f′(1) =
3.Medium
xyx = 0.5

Let f(x) = x2·e−x. Find f′(0.5).

f(x) = x2·e−xx = 0.5
f′(0.5) =
4.Medium
xyx = 1.5

Let f(x) = x·e2x. Find f′(1.5).

f(x) = x·e2xx = 1.5
f′(1.5) =
5.Hard
xy

Let f(x) = x3 + 6x2. Find the x-coordinate x of the local maximum.

f(x) = x3 + 6x2
x =
6.Hard
xyx = 2

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

f(x) = −x2 − 4x − 2x = 2
b =

Answer key

  1. 1. f′(1) = −21
  2. 2. f′(1) = −15
  3. 3. f′(0.5) = 0.4549
  4. 4. f′(1.5) = 80.34
  5. 5. x = −4
  6. 6. b = 2

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