Question

differentiate please..

y= √x +6 ÷ √x-6

Answer 1

`\bf y=\cfrac{√(x)+6}{√(x)-6}\implies \cfrac{dy}{dx}=\stackrel{quotient~rule}{\cfrac{(1)/(2)x^{-(1)/(2)}(√(x-6))~~-~~(√(x)+6)(1)/(2)x^{-(1)/(2)}}{(√(x)-6)^2}}`


`\bf \cfrac{dy}{dx}=\cfrac{(1)/(2)x^{-(1)/(2)}~(\underline{√(x)}-6~-~\underline{√(x)}-6)}{(√(x)-6)^2}\implies \cfrac{dy}{dx}=\cfrac{(1)/(2)x^{-(1)/(2)}(-12)}{(√(x)-6)^2} \\\\\\ \cfrac{dy}{dx}=\cfrac{(-12)/(2√(x))}{(√(x)-6)^2}\implies \cfrac{dy}{dx}=\cfrac{(-6)/(√(x))}{(√(x)-6)^2}\implies \cfrac{dy}{dx}=\cfrac{-6}{√(x)(√(x)-6)^2}`