Question

if y=a-x÷a+x find dy/dx

Answer 1

U=a-x
U'=a

V=a+x
V'=a

dy/dx=VU'-UV'/V^2
substituting we get

=2ax/(a+x)^2

Hope it helps you
Mark it as the brainlest please

Answer 2

Answer:

$\frac{d}{dx}$ $(\frac{a-x}{a+x})$ = $\frac{-2a}{(a+x)^2}$

Step-by-step explanation:

Given y = $\frac{a-x}{a+x}$

We have to find $\frac{dy}{dx}$

We know that $\frac{d}{dx}$ $(\frac{N}{D})$ = $\frac{D\frac{d}{dx}N - N\frac{d}{dx}D}{D^2}$

where N = Numerator

           D = Denominator

Therefore,  $\frac{dy}{dx}$ =  $\frac{d}{dx}$ $(\frac{a-x}{a+x})$

Using the above rule,

                 $\frac{dy}{dx}$  = $\frac{(a+x)(0 -1) - (a-x)(0+1)}{(a+x)^2}$

                      = $\frac{(a+x)( -1) - (a-x)(1)}{(a+x)^2}$

                      = $\frac{-a-x - a+x}{(a+x)^2}$

                      = $\frac{-2a}{(a+x)^2}$

Therefore,  $\frac{d}{dx}$ $(\frac{a-x}{a+x})$ = $\frac{-2a}{(a+x)^2}$