Find dy/dx yx = xy
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Naveen Sharma 8 years, 10 months ago
Ans. yx = xy
Take log both side, we get
log yx = log xy
=> x log y = y log x
differentiate w.r.t x, we get
=> \(x {1\over y} {dy \over dx} + log y = y {1\over x} + log x {dy \over dx}\)
=> \( {x\over y} {dy \over dx} - log x {dy \over dx} = {y\over x} - log y\)
=> \(( {{x\over y} - log x} ) {dy \over dx} = {y\over x} - log y\)
=> \( {dy \over dx} = { ( { {y\over x} - log y } ) \over ( {{x\over y} - log x} )}\)
2Thank You