Question

if x÷y-y÷x=a÷b and x÷y+y÷x=a-b find the value of "a"?​

Answer 1

$ANSWERS≈$

$given \: {x}^{y} + {y}^{x} = {a}^{b}$

$y \times {x}^{y - 1} + x \times {y}^{x - 1} \times \frac{dy}{dx} = 0$

Differentiating on both sides

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

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

Answer 2

Answer:

dy/dx = −y×x^y−1/x×y^x–1.

dy/dx = x×y^x−2/−y×x^y−2.

$thanks$