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) = 5x4 + x2 + 8x + 6. Find the slope of the graph at x = 3, that is f′(3).

f(x) = 5x4 + x2 + 8x + 6x = 3
f′(3) =
2.Easy
xyx = 1

Let f(x) = −5x4 − x2 + 5x + 6. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −5x4 − x2 + 5x + 6x = 1
f′(1) =
3.Medium
xyx = −2

Let f(x) = ln(x2 + 5). Find f′(−2).

f(x) = ln(x2 + 5)x = −2
f′(−2) =
4.Medium
xyx = 0

Let f(x) = (2x + 1)3. Find f′(0).

f(x) = (2x + 1)3x = 0
f′(0) =
5.Hard
xyx = −2

The tangent line to f(x) = 0.5x2 − 5x − 6 at x = −2 crosses the y-axis at y = b. Find b.

f(x) = 0.5x2 − 5x − 6x = −2
b =
6.Hard
xyx = −2

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

f(x) = −x2 + x + 5x = −2
b =

Answer key

  1. 1. f′(3) = 554
  2. 2. f′(1) = −17
  3. 3. f′(−2) = −0.4444
  4. 4. f′(0) = 6
  5. 5. b = −8
  6. 6. b = 9

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