Question

y=2x+3÷4x+5 find y"​(find the double derivative of y)​

Answer 1

Hope it was helpful.

Answer 2

Answer:     $\frac{16}{(4x+5)^3}$

Step-by-step explanation:

Given,

$y=\frac{2x+3}{4x+5}\\\;\\y=\frac{2(2x+3)}{2(4x+5)}\\\;\\y=\frac{4x+6}{2(4x+5)}\\\;\\y=\frac{4x+5+1}{2(4x+5)}\\\;\\y=\frac{4x+5}{2(4x+5)}+\frac{1}{2(4x+5)}\\\;\\y=\frac{1}{2}+\frac{1}{2(4x+5)}\\\;\\y=\frac{1}{2}+\frac{(4x+5)^{-1}}{2}\\\;\\\text{Diff. both sides with respect to x}\\\;\\\frac{dy}{dx}=0-\frac{(4x+5)^{-1-1}}{2}.\frac{d(4x+5)}{dx}\\\;\\\frac{dy}{dx}=-\frac{(4x+5)^{-2}}{2}.4\\\;\\\frac{dy}{dx}=-2(4x+5)^{-2}\\\;\\\text{Diff. both sides with respect to x}$

$\\\;\\\frac{d^2y}{dx^2}=-2.(-2).(4x+5)^{-2-1}.\frac{d(4x+5)}{dx}\\\;\\\frac{d^2y}{dx^2}=4(4x+5)^{-3}.4\\\;\\\frac{d^2y}{dx^2}=\frac{16}{(4x+5)^3}$