Differentiate the functions given w.r.t. x:(x−3)(x−4)(x−5)(x−1)(x−2)

Solution: Let y=(x−3)(x−4)(x−5)(x−1)(x−2)Taking log both sides,⇒lny=21ln[(x−3)(x−4)(x−5)(x−1)(x−2)]Differentiating both sides w.r.t. x,y1dxdy=21[x−11+x−21−x−31−x−41−x−51]⇒dxdy=2y[x−11+x−21−x−31−x−41−x−51]⇒dxdy=21(x−3)(x−4)(x−5)(x−1)(x−2)[x−11+x−21−x−31−x−41−x−51]

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Differentiate the functions given w.r.t. x: {{{{{({x}-{1})}{({

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Differentiate the functions given w.r.t. x:
$\frac{( x - 1 ) ( x - 2 )}{( x - 3 ) ( x - 4 ) ( x - 5 )}$

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Differentiate the functions given w.r.t. x:

\frac{( x - 1 ) ( x - 2 )}{( x - 3 ) ( x - 4 ) ( x - 5 )}

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Text solutionVerified

Solution: Let

y = \frac{( x - 1 ) ( x - 2 )}{( x - 3 ) ( x - 4 ) ( x - 5 )}

Taking log both sides,

\Rightarrow ln y = \frac{1}{2} ln [\frac{( x - 1 ) ( x - 2 )}{( x - 3 ) ( x - 4 ) ( x - 5 )}]

Differentiating both sides w.r.t. x,

\frac{1}{y} \frac{d y}{d x} = \frac{1}{2} [\frac{1}{x - 1} + \frac{1}{x - 2} - \frac{1}{x - 3} - \frac{1}{x - 4} - \frac{1}{x - 5}]

\Rightarrow \frac{d y}{d x} = \frac{y}{2} [\frac{1}{x - 1} + \frac{1}{x - 2} - \frac{1}{x - 3} - \frac{1}{x - 4} - \frac{1}{x - 5}]

\Rightarrow \frac{d y}{d x} = \frac{1}{2} \frac{( x - 1 ) ( x - 2 )}{( x - 3 ) ( x - 4 ) ( x - 5 )} [\frac{1}{x - 1} + \frac{1}{x - 2} - \frac{1}{x - 3} - \frac{1}{x - 4} - \frac{1}{x - 5}]

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Question Text	Differentiate the functions given w.r.t. x: $\frac{( x - 1 ) ( x - 2 )}{( x - 3 ) ( x - 4 ) ( x - 5 )}$
Answer Type	Text solution:1
Upvotes	150

Differentiate the functions given w.r.t. x:(x−3)(x−4)(x−5)(x−1)(x−2)​​

Text solutionVerified

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Differentiate the functions given w.r.t. x:
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