Mathematics 19 Online
OpenStudy (aravindg):

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

OpenStudy (anonymous):

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

OpenStudy (aravindg):

plz help

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

$\frac{du}{dx}+\frac{dv}{dx}=0$

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

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

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