Implicit differentiation

Intro

power rule d/dx(xn)=nx(n-1)
chain rule (f(g(x))’=f'(g(x)).g(x)

Sample Problem

Solution

√x.y=3
d/dx(√x.y)=d/dx(3) — defferentiate
d/dx(√x).y+√x.d/dx(y)=0
1/2.(1/√(x)).y+√x.1.dy/dx=0 — power rule and chain rule
y/2√x+√x.dy/dx=0 — simplify
√x.dy/dx=-y/2√x
dx/dy=-y/2. (√x. √x)
dy/dx=- y/2x