Question

If $x^y+y^x=a^b$, then find $\frac{dy}{dx}$.

Answer 1

Given $x^y+y^x=a^b$

$\Rightarrow y\times x^{y-1}+x\times y^{x-1}\times \frac{dy}{dx}=0$ ...Differentiating on both sides

$\Rightarrow \frac{dy}{dx}=\frac{-y\times x^{y-1}}{x\times y^{x-1}}\Rightarrow \frac{dy}{dx}=\frac{-y\times x^{y-2}}{x\times y^{x-2}}$