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) = −2x3 + 7x2 + x + 5. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −2x3 + 7x2 + x + 5x = −1
f′(−1) =
2.Easy
xyx = −3

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

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

Let f(x) = ln(3x2 + 4). Find f′(−1).

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

Let f(x) = x3·e−x. Find f′(2).

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

The tangent line to f(x) = 2x2 + 3x − 5 at x = −2 crosses the y-axis at y = b. Find b.

f(x) = 2x2 + 3x − 5x = −2
b =
6.Hard
xyx = 2

The tangent line to f(x) = 3x2 + 4x + 6 at x = 2 crosses the y-axis at y = b. Find b.

f(x) = 3x2 + 4x + 6x = 2
b =

Answer key

  1. 1. f′(−1) = −19
  2. 2. f′(−3) = −1256
  3. 3. f′(−1) = −0.8571
  4. 4. f′(2) = 0.5413
  5. 5. b = −13
  6. 6. b = −6

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