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) = x5 + x2 − 2x − 3. Find the slope of the graph at x = −1, that is f′(−1).

f(x) = x5 + x2 − 2x − 3x = −1
f′(−1) =
2.Easy
xyx = 1

Let f(x) = −4x5 − 5x2 − x + 6. Find the slope of the graph at x = 1, that is f′(1).

f(x) = −4x5 − 5x2 − x + 6x = 1
f′(1) =
3.Medium
xyx = 3

Let f(x) = ln(3x2 + 1). Find f′(3).

f(x) = ln(3x2 + 1)x = 3
f′(3) =
4.Medium
xyx = 1.5

Let f(x) = x·sin(3x), with x in radians. Find f′(1.5).

f(x) = x·sin(3x)x = 1.5 rad
f′(1.5) =
5.Hard
xyx = 2

The tangent line to f(x) = x2 + 3x + 6 at x = 2 crosses the y-axis at y = b. Find b.

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

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

f(x) = −x2 + 4x − 3x = 1
b =

Answer key

  1. 1. f′(−1) = 1
  2. 2. f′(1) = −31
  3. 3. f′(3) = 0.6429
  4. 4. f′(1.5) = −1.926
  5. 5. b = 2
  6. 6. b = −2

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