If y-x logx-a-b x- then xnd2 y-d x2-x d y-d x-ym- where-A- n-3- m-2B- n-2- m-3C- m-n-2D- m-n-3

The correct option is A y = x log x/(a+bx) = x log x x log (a+bx) dy/dx = (log x) + 1 log (a+bx) bx/a+bx d^2y/dx^2 = 1/x b/a+bx b(a+bx) b^2x/(a+bx)^2 = ...

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Byju's Answer

Standard XI

Mathematics

Logarithmic Inequalities

If y=x logx/a...

Question

If $y = x l o g \frac{x}{(a + b x)}$ , then $x^{n} \frac{d^{2} y}{d x^{2}} = {(x \frac{d y}{d x} - y)}^{m}$ , where:

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Solution

The correct option is A

$y = x l o g \frac{x}{(a + b x)}$
$= x l o g x - x l o g (a + b x)$
$\frac{d y}{d x} = (l o g x) + 1 - l o g (a + b x) \frac{- b x}{a + b x}$
$\frac{d^{2} y}{d x^{2}} = \frac{1}{x} - \frac{b}{a + b x} \frac{- b (a + b x) - b^{2} x}{(a + b x)^{2}}$
$= \frac{a^{2}}{x (a + b)^{2}}$
$\frac{x^{n} d^{2} y}{d x^{2}} = \frac{a^{2} x^{n - 1}}{(a + v x)^{2}}$
${(\frac{x d y}{d x^{- y}})}^{m} = \frac{a^{m} x^{m}}{(a + b x)^{m}}$
$c o m p a r i n g u s e g e t m = 2, n = 3$

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If y=xlogx(a+bx) , then xnd2ydx2=(xdydx−y)m, where:

The correct option is A y=x logx(a+bx) =x logx−x log (a+bx) dydx=(logx)+1−log(a+bx)−bxa+bx d2ydx2=1x−ba+bx−b(a+bx)−b2x(a+bx)2 =a2x(a+b)2 xnd2ydx2=a2xn−1(a+vx)2 (x dydx−y)m=amxm(a+bx)m comparing use get m=2,n=3

If $y = x l o g \frac{x}{(a + b x)}$ , then $x^{n} \frac{d^{2} y}{d x^{2}} = {(x \frac{d y}{d x} - y)}^{m}$ , where: