Question

найти производную dx/dy

y^2+e^(xy)-x^2=0

Answer 1

$frac{dx}{dy}=?\\y^2+e^{xy}-x^2=0\\x=x(y); ; to ; ; y'=1\\2y+e^{xy}cdot (xy)'-2xx'=0\\2y+e^{xy}cdot (x'y+xy')-2xx'=0\\2y+e^{xy}cdot (x'y+xcdot 1)-2xx'=0\\2y+e^{xy}cdot x'y+xcdot e^{xy}-2xx'=0\\x'cdot (ye^{xy}-2x)=-2y-xe^{xy}\\x'=frac{dx}{dy}=-frac{2y+xe^{xy}}{ye^{xy}-2x}$