Question

How do you find the derivative of `sqrtx+sqrty=9`?

Answer 1

`dy/dx=-sqrt(y/x)`

Explanation:

`sqrt(x)+sqrt(y)=9`

By rewriting a bit,

`Rightarrow x^(1/2)+y^(1/2)=9`

By differentiating with respect to `x`,

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

By cleaning up a bit,

`Rightarrow 1/(2sqrt(x))+1/(2sqrt(y))dy/dx=0`

By subtracting `1/(2sqrt(x))` from both sides,

`1/(2sqrt(y))dy/dx=-1/(2sqrt(x))`

By multiplying both sides by `2sqrt(y)`,

`dy/dx=-(cancel(2)sqrt{y})/(cancel(2)sqrt(x))=-\sqrt(y/x)`

I hope that this was clear.