If Xm . Yn = (x + Y)m+n, Then Show That Dydxdydx=yx

0Tamil Nadu Board of Secondary EducationHSC Commerce Class 11Question PapersQuestion PapersTextbook Solutions7033MCQ Online Mock TestsImportant SolutionsConcept Notes12Time TablesSyllabusIf xm . yn = (x + y)m+n, then show that dydxdydx=yx - Business Mathematics and Statistics
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Question

If xm . yn = (x + y)m+n, then show that `"dy"/"dx" = y/x`

Sum

SolutionShow Solution

xm . yn = (x + y)m+n

Taking logarithm on both sides we get,

m log x + n log y = (m + n) log(x + y)

Differentiating with respect to x,

`m1/x + n1/y "dy"/"dx" = (m + n) 1/(x + y)(1 + "dy"/"dx")`

`"dy"/"dx"(n/y - (m + n)/(x + y)) = (m + n)/(x + y) - m/x`

`"dy"/"dx" ((nx + ny - my - ny)/(y(x + y))) = ((mx + nx - mx - my)/(x(x + y)))`

`"dy"/"dx" ((nx - my)/(y(x + y))) = (nx - my)/(x(x + y))`

`"dy"/"dx" = y/x`

Hence proved.

shaalaa.comDifferentiation Techniques Report Error Is there an error in this question or solution? Q 2Q 1. (iv)Q 1. (i)Chapter 5: Differential Calculus - Exercise 5.7 [Page 120]

APPEARS IN

Tamil Nadu Board Samacheer Kalvi Class 11th Business Mathematics and Statistics Answers GuideChapter 5 Differential CalculusExercise 5.7 | Q 2 | Page 120

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