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OpenStudy (aravindg):

find dy/dx if x^y+y^x=a^b find dy/dx if x^y+y^x=a^b @Mathematics

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OpenStudy (anonymous):

sorry aravind, gtg; was just checking something from last night :{

OpenStudy (aravindg):

plz help

OpenStudy (diyadiya):

ok take .. u=y^x and v=x^y and u + v=a^b

OpenStudy (diyadiya):

\[\frac{du}{dx}+\frac{dv}{dx}=0\]

OpenStudy (diyadiya):

\[\frac{du}{dx}+\frac{dv}{dx}=0 --- (1)\] u=y^x log u=x log y differentiating w.r.t x, on both sides \[\frac{1}{u}\frac{du}{dx}=x \frac{d}{dx} (logy) + \log y \frac{d}{dx}(x)\] \[=x \frac{1}{y}\frac{dy}{dx}+logy\] \[\frac{du}{dx}=u \left[ \frac{x}{y}\frac{dy}{dx}+logy \right]\] \[\frac{du}{dx}=y^x \left[ \frac{x}{y}\frac{dy}{dx}+logy \right] --(2)\]

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OpenStudy (diyadiya):

similarly take log v= y logx and substitute it in equation (1) and get the answer :)

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