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) = −2x5 + 8x2 + 5x − 3. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = −2x5 + 8x2 + 5x − 3x = −3
f′(−3) =
2.Easy
xyx = −3

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

f(x) = 3x3 − 5x2 − 5x = −3
f′(−3) =
3.Medium
xyx = 1

Let f(x) = x3·e−x. Find f′(1).

f(x) = x3·e−xx = 1
f′(1) =
4.Medium
xyx = −2

Let f(x) = ln(x2 + 2). Find f′(−2).

f(x) = ln(x2 + 2)x = −2
f′(−2) =
5.Hard
xyx = 3

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

f(x) = x2 + x − 1x = 3
b =
6.Hard
xyx = −1

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

f(x) = x2 − x + 2x = −1
b =

Answer key

  1. 1. f′(−3) = −853
  2. 2. f′(−3) = 111
  3. 3. f′(1) = 0.7358
  4. 4. f′(−2) = −0.6667
  5. 5. b = −10
  6. 6. b = 1

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