Quick Revision Reference

Chain rule: d/dx[f(g(x))] = f'(g(x)) * g'(x) — MOST IMPORTANT RULE
All "co-" derivatives are NEGATIVE
For f(x)^g(x): use logarithmic differentiation
Inverse trig: SIMPLIFY FIRST (substitute x = $\frac{sin}{cos}$ /tan t)
Domain trap: sin^(-1)(sin 2t) = 2t only if |2t| <= pi/2
Parametric: dy/dx = $\frac{dy/dt}{(dx/dt)}$
Parametric $d^{2y}$ / $dx^2$ = [d/dt $\frac{dy}{dx}$ ]/ $\frac{dx}{dt}$ NOT $\frac{d^2y/dt^2}{(d^2x/dt^2)}$
Implicit: d/dx( $y^n$ ) = n*y^(n-1)*dy/dx
Differentiable => Continuous (converse FALSE)
|x| NOT differentiable at 0; | $x^3$ | IS differentiable at 0
tan^(-1)(2 $\frac{x}{1-x^2}$ ) = 2tan^(-1)(x) for |x| < 1
(uv)^(n) = sum C(n,r)*u^(n-r)*v^(r) — Leibniz
d/dx(sin^(-1) x) = 1/sqrt(1- $x^2$ ); d/dx(tan^(-1) x) = $\frac{1}{1+x^2}$
ln(fg) = ln f + ln g simplifies products for differentiation
d/dx[cos^(-1)(cos x)] depends on the interval: x or 2pi-x