AP Calculus Differentiation Rules

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Last updated 3:39 PM on 8/26/26
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17 Terms

1
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Power Rule

y = xⁿ

y' = nxⁿ⁻¹

2
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Product Rule

y = uv

y' = uv' + vu'

3
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Quotient Rule

y = u / v

y' = (vu' - uv') / v²

4
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Chain Rule

y = g(f(x))

y' = g'(f(x)) * f'(x)

5
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y = sin(x)

y' = cos(x)

6
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y = cos(x)

y' = -sin(x)

7
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y = tan(x)

y' = sec²(x)

8
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y = cot(x)

y' = -csc²(x)

9
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y = sec(x)

y' = sec(x)tan(x)

10
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y = csc(x)

y' = -csc(x)cot(x)

11
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y = sin⁻¹(u)

y' = (1 / √(1 - u²)) * (du / dx)

12
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y = tan⁻¹(u)

y' = (1 / (1 + u²)) * (du / dx)

13
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y = cos⁻¹(u)

y' = (-1 / √(1 - u²)) * (du / dx)

14
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y = e^u

y' = (e^u) * (du / dx)

15
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y = a^u

y' = a^u * ln(a) * (du / dx)

16
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y = ln(u)

y' = (1 / u) * (du / dx)

17
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y = log∨a (u)

y' = (1 / u * ln(a)) * (du / dx)