The value of d y-d x if y-x-12x-23 is equal toA- y x-12-x-23B- y -2x-1-3x-2C- 2 x -1- x -23D- y 2 x-1-3 x-2

The correct option is D y2x 1+3x+2y = (x – 1)^2 (x+2)^3 Taking logarithm,nbsp;ln y = 2 ln(x 1)+3 ln(x+2) Differentiating both sides. 1/y.y'=2/(x 1)+3/x+2 (Chain ...

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Standard XII

Mathematics

Logarithmic Differentiation

The value of ...

Question

The value of $\frac{d y}{d x} i f y = (x - 1)^{2} (x + 2)^{3}$ is equal to

y (\frac{x - 1}{2} + \frac{x + 2}{3}]

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y . (2 (x - 1) + 3 (x + 2)]

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\frac{2}{x - 1} + \frac{x + 2}{3}

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y (\frac{2}{x - 1} + \frac{3}{x + 2}]

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Solution

The correct option is D $y (\frac{2}{x - 1} + \frac{3}{x + 2}]$
$y = (x - 1)^{2} (x + 2)^{3}$

Taking logarithm, $l n y = 2 l n (x - 1) + 3 l n (x + 2)$

Differentiating both sides.

$\frac{1}{y} . y^{'} = \frac{2}{(x - 1)} + \frac{3}{x + 2}$ (Chain rule is applied on the LHS)

$y^{'} = y [\frac{2}{x - 1} + \frac{3}{x + 2}]$

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The value of dydx if y=(x−1)2(x+2)3 is equal to

The correct option is D y(2x−1+3x+2]y=(x–1)2(x+2)3 Taking logarithm,ln y=2 ln(x−1)+3 ln(x+2) Differentiating both sides. 1y.y′=2(x−1)+3x+2 (Chain rule is applied on the LHS) y′=y[2x−1+3x+2]

The value of $\frac{d y}{d x} i f y = (x - 1)^{2} (x + 2)^{3}$ is equal to