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) = −5x3 − 4x2 − 7x + 5. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −5x3 − 4x2 − 7x + 5x = 2
f′(2) =
2.Easy
xyx = −2

Let f(x) = x5 − 4x2 + 5x − 1. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = x5 − 4x2 + 5x − 1x = −2
f′(−2) =
3.Medium
xyx = 1

Let f(x) = x·sin(x), with x in radians. Find f′(1).

f(x) = x·sin(x)x = 1 rad
f′(1) =
4.Medium
xyx = 1.5

Let f(x) = x3·e2x. Find f′(1.5).

f(x) = x3·e2xx = 1.5
f′(1.5) =
5.Hard
xyx = 1

The tangent line to f(x) = −x2 − 2x at x = 1 crosses the y-axis at y = b. Find b.

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

The tangent line to f(x) = 0.5x2 − 2x − 2 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − 2x − 2x = 1
b =

Answer key

  1. 1. f′(2) = −83
  2. 2. f′(−2) = 101
  3. 3. f′(1) = 1.382
  4. 4. f′(1.5) = 271.2
  5. 5. b = 1
  6. 6. b = −2.5

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