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Calculus — Derivatives

Rules and formulas for differentiation

M
mathlete_2026 15 terms Mar 10, 2026
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Terms 15

1
Power Rule
d/dx[x^n] = n·x^(n-1)
2
Product Rule
d/dx[f·g] = f'g + fg'
3
Quotient Rule
d/dx[f/g] = (f'g − fg') / g²
4
Chain Rule
d/dx[f(g(x))] = f'(g(x)) · g'(x)
5
Derivative of sin(x)
cos(x)
6
Derivative of cos(x)
−sin(x)
7
Derivative of e^x
e^x
8
Derivative of ln(x)
1/x
9
Derivative of tan(x)
sec²(x)
10
Critical Point
Where f'(x) = 0 or is undefined; possible max or min
11
Inflection Point
Where concavity changes; f''(x) changes sign
12
Implicit Differentiation
Differentiating both sides when y is not isolated
13
Related Rates
Using derivatives to relate rates of change between variables
14
Mean Value Theorem
There exists c in (a,b) where f'(c) = [f(b)−f(a)]/(b−a)
15
L'Hôpital's Rule
For 0/0 or ∞/∞ forms: lim f/g = lim f'/g'