calculus

What I do

• Compute derivatives and integrals of functions
• Apply differentiation rules (product, chain, quotient)
• Solve optimization problems using derivatives
• Evaluate definite and improper integrals
• Apply Taylor series expansions
• Solve differential equations

When to use me

When analyzing rates of change, finding optimal values, or computing areas and accumulations.

Key Concepts

• Derivative: f'(x) = lim_{h→0} (f(x+h) - f(x))/h
• Chain Rule: (f∘g)' = (f'∘g)g'
• Fundamental Theorem: ∫_a^b f'(x)dx = f(b) - f(a)
• Taylor Series: f(x) = Σ f^{(n)}(a)/n! (x-a)^n
• Integration by Parts: ∫u dv = uv - ∫v du
• L'Hôpital's Rule: lim f/g = lim f'/g' for indeterminate forms