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) = −2x4 + 8x2 − 4x + 1. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −2x4 + 8x2 − 4x + 1x = 3
f′(3) =
2.Easy
xyx = −1

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

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

Let f(x) = x3·e−0.5x. Find f′(1).

f(x) = x3·e−0.5xx = 1
f′(1) =
4.Medium
xyx = −2

Let f(x) = ln(x2 + 5). Find f′(−2).

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

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

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

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

f(x) = x2 + 2x + 1x = 2
b =

Answer key

  1. 1. f′(3) = −172
  2. 2. f′(−1) = −31
  3. 3. f′(1) = 1.516
  4. 4. f′(−2) = −0.4444
  5. 5. b = −27
  6. 6. b = −3

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