Question

If y=(2x+3)/(4x+5) ,then find y"​

Answer 1

hope It will help you

Answer 2

The value y'' is $y''=\frac{16}{\left(4x+5\right)^3}$

Step-by-step explanation:

Consider the provided equation.

$y=\frac{2x+3}{4x+5}$

Apply the quotient rule: $\frac{d}{dx}[\frac{f(x)}{g(x)}] =\frac{f'(x)g(x)-g'(x)f(x)}{(g(x))^2}$

$y'=\frac{\frac{d}{dx}\left(2x+3\right)\left(4x+5\right)-\frac{d}{dx}\left(4x+5\right)\left(2x+3\right)}{\left(4x+5\right)^2}$

$y'=\frac{2\left(4x+5\right)-4\left(2x+3\right)}{\left(4x+5\right)^2}$

$y'=\frac{8x+10-8x-12}{\left(4x+5\right)^2}$

$y'=-\frac{2}{\left(4x+5\right)^2}$

Again differentiate the equation.

$y''=-2\frac{d}{dx}\left(\frac{1}{\left(4x+5\right)^2}\right)$

$y''=-2\frac{d}{dx}\left(\left(4x+5\right)^{-2}\right)$

$y''=-2(-2)(4x+5)^{-3}\cdot4$

$y''=-2\left(-\frac{2}{\left(4x+5\right)^3}\right)\cdot \:4$

$y''=\frac{16}{\left(4x+5\right)^3}$

The value y'' is $y''=\frac{16}{\left(4x+5\right)^3}$

#Learn more

Function and differentiation

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