Question

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

Answer 1

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

Answer 2

plz help

Answer 3

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

Answer 4

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

Answer 5

\[\frac{du}{dx}+\frac{dv}{dx}=0 --- (1)\]
u=y^x
log u=x log y

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

Answer 6

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