Question

Find dy/dx of the functions.
y^{x}=x^{y}

Answer 1

Step-by-step explanation:

y^(x) = x^(y)

taking log on both the sides

log y^(x) = log x^(y)

x log y = y log x { log m^n = n log m }

Now, differentiating both the sides with respect to x using chain rule.

x/y dy/dx + log y = y. 1/x + log x dy/dx

log y - y/x = log x dy/dx - x/y dy/dx

(x log y - y) / y = {(y log x - x) / y } dy/dx

dy/dx = {(x log y - y) / x } / {(y log x - x)/y}

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

Hope this will helpful for you...!!!!!