Question

y=3x+4÷4x+5 find the differentition
​

Answer 1

Answer:

$\frac{dy}{dx}=\frac{-1}{(4x+5)^2}$

Explanation:

Given, $y = \frac{3x+4}{4x+5}$ .

We know that

If $y=\frac{f(x)}{g(x)}$ then $\frac{dy}{dx}=\frac{g(x)\frac{d(f(x))}{dx}-f(x)\frac{d(g(x))}{dx} }{g(x)^2}$.

Therefore,

$\frac{dy}{dx}=\frac{(4x+5)\frac{d(3x+4))}{dx}-(3x+4)\frac{d(4x+5)}{dx} }{(4x+5)^2}$

$\frac{dy}{dx} =\frac{(4x+5)3-(3x+4)4}{(4x+5)^2}$

$\frac{dy}{dx} = \frac{12x+15-12x-16}{(4x+5)^2}$

$\frac{dy}{dx}=\frac{-1}{(4x+5)^2}$