🔢 Key equations
Math
Foundational Concepts
Limit definition
\lim_{x \to a} f(x) = L
Derivative
f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}
Differentiation Rules and Applications
Power Rule
\frac{d}{dx} x^n = n x^{n-1}
Product Rule
\frac{d}{dx} [u(x) v(x)] = u'(x) v(x) + u(x) v'(x)
Quotient Rule
\frac{d}{dx} \left[ \frac{u(x)}{v(x)} \right] = \frac{u'(x) v(x) - u(x) v'(x)}{[v(x)]^2}
Chain Rule
\frac{d}{dx} f(g(x)) = f'(g(x)) g'(x)
Integrals
Basic Integral
\int_a^b f(x) \, dx
Fundamental Theorem of Calculus
\int_a^b f(x) \, dx = F(b) - F(a)
Integration by Parts
\int u(x) v'(x) dx = u(x) v(x) - \int u'(x) v(x) dx
Substitution Rule
\int f(g(x)) g'(x) \, dx = \int f(u) \, du
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