Tamil Nadu Board of Secondary EducationHSC Commerce Class 11

If xy . yx , then prove that dydxdydx=yx(xlogy-yylogx-x) - Business Mathematics and Statistics

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Sum

If xy . yx , then prove that `"dy"/"dx" = y/x((x log y - y)/(y log x - x))` 

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Solution

Given xy . y

Taking logarithm on both sides we get,

y log x = x log y

Differentiating with respect to 'x' we get,

`y*1/x + log x * "dy"/"dx" = x * 1/y "dy"/"dx" + log y(1)`

`=> y/x + log x ("dy"/"dx") = x/y "dy"/"dx" + log y`

`=> "dy"/"dx" (log x - x/y) = log y - y/x`

`=> "dy"/"dx" ((y log x - x)/y) = (x log y - y)/x`

`=> "dy"/"dx" = (x log y - y)/x xx y/(y log x - x)`

`=> "dy"/"dx" = y/x((x log y - y)/(y log x - x))`

Hence proved.

Concept: Differentiation Techniques
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Chapter 5: Differential Calculus - Miscellaneous Problems [Page 125]

APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 11th Business Mathematics and Statistics Answers Guide
Chapter 5 Differential Calculus
Miscellaneous Problems | Q 7 | Page 125
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