Tamil Nadu Board of Secondary EducationHSC Commerce Class 11

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

Sum

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

#### 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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