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 + 7x − 6. Find the slope of the graph at x = 3, that is f′(3).

f(x) = 5x5 − 7x2 + 7x − 6x = 3
f′(3) =
2.Easy
xyx = −3

Let f(x) = x5 − 9x2 − 3x − 6. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = x5 − 9x2 − 3x − 6x = −3
f′(−3) =
3.Medium
xyx = 1.5

Let f(x) = x3·ex. Find f′(1.5).

f(x) = x3·exx = 1.5
f′(1.5) =
4.Medium
xyx = 1.5

Let f(x) = x3·e−x. Find f′(1.5).

f(x) = x3·e−xx = 1.5
f′(1.5) =
5.Hard
xyx = 2

The tangent line to f(x) = x2 + x + 6 at x = 2 crosses the y-axis at y = b. Find b.

f(x) = x2 + x + 6x = 2
b =
6.Hard
xyx = 1

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

f(x) = 0.5x2 − x + 1x = 1
b =

Answer key

  1. 1. f′(3) = 1990
  2. 2. f′(−3) = 456
  3. 3. f′(1.5) = 45.38
  4. 4. f′(1.5) = 0.7531
  5. 5. b = 2
  6. 6. b = 0.5

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