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 = 2

Let f(x) = −2x4 + 7x2 + 7x. Find the slope of the graph at x = 2, that is f′(2).

f(x) = −2x4 + 7x2 + 7xx = 2
f′(2) =
2.Easy
xyx = −2

Let f(x) = −4x5 + 7x2 − 6x + 4. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −4x5 + 7x2 − 6x + 4x = −2
f′(−2) =
3.Medium
xyx = 2

Let f(x) = ln(x2 + 2). Find f′(2).

f(x) = ln(x2 + 2)x = 2
f′(2) =
4.Medium
xyx = 1.5

Let f(x) = x·sin(2x), with x in radians. Find f′(1.5).

f(x) = x·sin(2x)x = 1.5 rad
f′(1.5) =
5.Hard
xyx = 2

The tangent line to f(x) = 2x2 + 4x + 3 at x = 2 crosses the y-axis at y = b. Find b.

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

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

f(x) = 3x2 − 3x + 3x = 3
b =

Answer key

  1. 1. f′(2) = −29
  2. 2. f′(−2) = −354
  3. 3. f′(2) = 0.6667
  4. 4. f′(1.5) = −2.829
  5. 5. b = −5
  6. 6. b = −24

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