Question

find dy/dx if x^m•y^n=x^m+y^n​

Answer 1

Answer:

$x {}^{m} .y {}^{n} = x {}^{m } + y {}^{n} \\ \\ diff \: .with .\: respect .\: to. \: x \: \\ \\ x {}^{m - 1} .y {}^{n} + x {}^{m}. y {}^{n - 1} . \frac{dy}{dx} = x {}^{m - 1} + y {}^{n - 1} . \frac{dy}{dx} \\ \\ = > \frac{dy}{dx} (x {}^{m} .y {}^{n - 1} - y {}^{n - 1} ) = x {}^{m - 1} - x {}^{m - 1} .y {}^{n} \\ \\ = > \frac{dy}{dx} = \frac{x {}^{m - 1} (1 - y {}^{n} )}{y {}^{n - 1} (x {}^{m} - 1) } \\ \\ \\ \\ formula \: \: - \: \: \frac{d}{dx} (x) = 1 \\ \\ \\ \frac{d}{dx}( x {}^{2} ) = 2x$