Question

If xy.yx = m , m is constant then dy/dx
is equal to

Answer 1

Step-by-step explanation:

Given If xy . yx  = M, where M is constant then dy  / dx is equal to

Now x^y x y^x = M (given)

Taking log on both sides we get

So log x^y . y^x = log M

So log x^y + log y^x = log M

So y log x + x log y = log M

Differentiating with respect to x

So y/x + log x dy/dx + x/y dy/dx + log y = 0

So dy/dx (x/y + log x) = - log y – y/x

So dy/dx = - (x log y + y / x) / (x + y log x / y)

Or dy/dx = - y/x (x log y + y / y log x + x)