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) = −4x3 − 5x2 − 6x + 2. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = −4x3 − 5x2 − 6x + 2x = −1
f′(−1) =
2.Easy
xyx = 1

Let f(x) = 4x3 − 6x2 − 7x + 5. Find the slope of the graph at x = 1, that is f′(1).

f(x) = 4x3 − 6x2 − 7x + 5x = 1
f′(1) =
3.Medium
xyx = 2

Let f(x) = ln(3x2 + 5). Find f′(2).

f(x) = ln(3x2 + 5)x = 2
f′(2) =
4.Medium
xyx = 2

Let f(x) = (4x + 5)4. Find f′(2).

f(x) = (4x + 5)4x = 2
f′(2) =
5.Hard
xyx = −2

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

f(x) = −x2 − 2x − 3x = −2
b =
6.Hard
xyx = 1

The tangent line to f(x) = 2x2 + 5x + 1 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 2x2 + 5x + 1x = 1
b =

Answer key

  1. 1. f′(−1) = −8
  2. 2. f′(1) = −7
  3. 3. f′(2) = 0.7059
  4. 4. f′(2) = 35152
  5. 5. b = 1
  6. 6. b = −1

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