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) = 5x5 + x2 − 7. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = 5x5 + x2 − 7x = −2
f′(−2) =
2.Easy
xyx = −2

Let f(x) = 5x5 + 8x2 − 3x + 6. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = 5x5 + 8x2 − 3x + 6x = −2
f′(−2) =
3.Medium
xyx = 1

Let f(x) = x·sin(2x), with x in radians. Find f′(1).

f(x) = x·sin(2x)x = 1 rad
f′(1) =
4.Medium
xyx = 0.5

Let f(x) = x·sin(x), with x in radians. Find f′(0.5).

f(x) = x·sin(x)x = 0.5 rad
f′(0.5) =
5.Hard
xyx = 1

The tangent line to f(x) = 2x2 − 4x + 1 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 2x2 − 4x + 1x = 1
b =
6.Hard
xyx = 1

The tangent line to f(x) = 3x2 + 4x − 2 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = 3x2 + 4x − 2x = 1
b =

Answer key

  1. 1. f′(−2) = 396
  2. 2. f′(−2) = 365
  3. 3. f′(1) = 0.077
  4. 4. f′(0.5) = 0.9182
  5. 5. b = −1
  6. 6. b = −5

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