Question

How do you differentiate `x^(2/3)+y^(2/3)=pi^(2/3)`?

Answer 1

Differential is `-root(3)(x/y)`

Explanation:

Differential of `x^n` is `nx^(n-1)` and that of `y^n`, is `ny^(n-1)(dy)/(dx)` using implicit differentiation. Also as `pi` is a constant, its differential, or that of any of its power, is `0`

Hence differential of `x^(2/3)+y^(2/3)=pi^(2/3)`

is `2/3x^(-1/3)+2/3y^(-1/3)(dy)/(dx)=0`

and `(dy)/(dx)=-(2/3y^(-1/3))/(2/3x^(-1/3))=-(1/root(3)y)/(1/root(3)x)`

= `-root(3)(x/y)`