Question

If xy . yx

= M, where 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)

Reference link will be

https://brainly.in/question/18319292

Answer 2

Step-by-step explanation:

Given x

${x}^{y} \times {y}^{x} = m \\ where \: m \: i s \: constant \\ \\ taking \: log \: o n \: both \: sides \\ log( {x}^{y} \times {y}^{x)} = log \: m \\ \\ \\ for \: remaining \: solution \: please \: see \: the \: image$