Cue Column: Key Questions

• What are the 6 main differentiation techniques?
• When to use logarithmic differentiation?
• How to handle inverse trig derivatives?
• What is the chain rule pattern?

Notes Column: Differentiation in JEE requires mastery of six techniques: (1) direct formula application, (2) chain rule, (3) product/quotient rules, (4) implicit differentiation, (5) parametric differentiation, (6) logarithmic differentiation.

The chain rule d/dx[f(g(x))] = f'(g(x)) * g'(x) is the most critical. It extends to nested compositions: d/dx[f(g(h(x)))] = f'(g(h(x))) * g'(h(x)) * h'(x).

For inverse trig problems, ALWAYS simplify the expression using trigonometric substitution BEFORE differentiating. This transforms complex derivative computations into trivial ones.

Logarithmic differentiation is mandatory for f(x)^g(x) forms (like $x^x$, x^(sin x), (sin x)^x). Take ln of both sides, differentiate implicitly, then multiply by y.

Parametric differentiation: dy/dx = $\frac{dy/dt}{(dx/dt)}$. For the second derivative: $d^{2y}$/$dx^2$ = [d/dt$\frac{dy}{dx}$] / $\frac{dx}{dt}$. Do NOT write $d^{2y}$/$dx^2$ = $\frac{d^2y/dt^2}{(d^2x/dt^2)}$ — this is WRONG.

Summary: Master chain rule and inverse trig simplification — these cover 70% of JEE differentiation. Logarithmic differentiation handles the remaining exotic forms. Always simplify before differentiating.