Question

If x^y × y^x = e^x^2 then dy/dx at x=1 is equal to??

Answer 1

Take natural log of both sides, then differentiate implicitly.

xy=yx

ylnx=xlny

yx+lnxdydx=xydydx+lny

Multiply both sides by xy

y2+xylnxdydx=x2dydx+xylny

x2dydx−xylnxdydx=y2−xylny

x(x−ylnx)dydx=y(y−xlny)

dydx=y(y−xlny)x(x−ylnx)

Answer 2

hope it helps uhh mate........