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 = −3

Let f(x) = x4 − 5x2 − 3x + 8. Find the slope of the graph at x = −3, that is f′(−3).

f(x) = x4 − 5x2 − 3x + 8x = −3
f′(−3) =
2.Easy
xyx = −2

Let f(x) = −x3 + 4x2 + 7x + 6. Find the slope of the graph at x = −2, that is f′(−2).

f(x) = −x3 + 4x2 + 7x + 6x = −2
f′(−2) =
3.Medium
xyx = 1.5

Let f(x) = x·ex. Find f′(1.5).

f(x) = x·exx = 1.5
f′(1.5) =
4.Medium
xyx = −2

Let f(x) = ln(3x2 + 1). Find f′(−2).

f(x) = ln(3x2 + 1)x = −2
f′(−2) =
5.Hard
xyx = 1

The tangent line to f(x) = −x2 − 5x + 3 at x = 1 crosses the y-axis at y = b. Find b.

f(x) = −x2 − 5x + 3x = 1
b =
6.Hard
xyx = −1

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

f(x) = 3x2 + 4x + 4x = −1
b =

Answer key

  1. 1. f′(−3) = −81
  2. 2. f′(−2) = −21
  3. 3. f′(1.5) = 11.2
  4. 4. f′(−2) = −0.9231
  5. 5. b = 4
  6. 6. b = 1

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