Differentiation

The rate of change measures how

The rate of change measures how one quantity changes with respect to another. For example, if a car travels from Mumbai to Pune, its speed is the rate

The derivative of a function f(x)

The derivative of a function f(x) at point x=a is defined as f'(a) = lim(h→0) [f(a+h) - f(a)]/h, provided this limit exists. This represents the insta

The method of finding derivatives directly

The method of finding derivatives directly from the definition: f'(x) = lim(h→0) [f(x+h) - f(x)]/h. This involves: (1) Finding f(x+h), (2) Computing f

Key derivative formulas derived using first

Key derivative formulas derived using first principles: (1) d/dx(xⁿ) = nxⁿ⁻¹, (2) d/dx(sin x) = cos x, (3) d/dx(cos x) = -sin x, (4) d/dx(tan x) = sec

Four main rules

Four main rules: (1) Sum/Difference Rule: d/dx[f(x) ± g(x)] = f'(x) ± g'(x), (2) Product Rule: d/dx[f(x)·g(x)] = f'(x)·g(x) + f(x)·g'(x), (3) Quotient