Question

найти производную dx/dy

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

Answer 1

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