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) = −5x4 + 7x2 − 4x − 3. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −5x4 + 7x2 − 4x − 3x = 1
f′(1) =
2.Easy
xyx = 3

Let f(x) = −2x5 − 3x2 + 8x − 6. Find the slope of the graph at x = 3, that is f′(3).

f(x) = −2x5 − 3x2 + 8x − 6x = 3
f′(3) =
3.Medium
xyx = −1

Let f(x) = ln(2x2 + 5). Find f′(−1).

f(x) = ln(2x2 + 5)x = −1
f′(−1) =
4.Medium
xyx = 2

Let f(x) = ln(3x2 + 5). Find f′(2).

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

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

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

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

f(x) = 3x2 − 5x + 2x = 2
b =

Answer key

  1. 1. f′(1) = −10
  2. 2. f′(3) = −820
  3. 3. f′(−1) = −0.5714
  4. 4. f′(2) = 0.7059
  5. 5. b = −5
  6. 6. b = −10

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