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) = −x3 + 8x2 + 9x − 8. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −x3 + 8x2 + 9x − 8x = 1
f′(1) =
2.Easy
xyx = −3

Let f(x) = 4x4 − 5x2 − 7x − 9. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = 4x4 − 5x2 − 7x − 9x = −3
f′(−3) =
3.Medium
xyx = 3

Let f(x) = ln(x2 + 5). Find f′(3).

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

Let f(x) = ln(3x2 + 1). Find f′(1).

f(x) = ln(3x2 + 1)x = 1
f′(1) =
5.Hard
xyx = 2

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

f(x) = −x2 + 2x − 5x = 2
b =
6.Hard
xyx = 1

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

f(x) = −x2 + 2x + 1x = 1
b =

Answer key

  1. 1. f′(1) = 22
  2. 2. f′(−3) = −409
  3. 3. f′(3) = 0.4286
  4. 4. f′(1) = 1.5
  5. 5. b = −1
  6. 6. b = 2

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