Use implicit differentiation where LaTeX: \displaystyle y is a function of LaTeX: \displaystyle x to find the derivative of LaTeX: \displaystyle - 2 e^{x^{2}} e^{y^{2}} + 4 \sin{\left(x^{2} \right)} \cos{\left(y^{2} \right)}=17

Taking the derivative of both sides using implicit differentiation gives: LaTeX: - 4 x e^{x^{2}} e^{y^{2}} + 8 x \cos{\left(x^{2} \right)} \cos{\left(y^{2} \right)} - 4 y y' e^{x^{2}} e^{y^{2}} - 8 y y' \sin{\left(x^{2} \right)} \sin{\left(y^{2} \right)} = 0 Solving for LaTeX: \displaystyle y' gives LaTeX: \displaystyle y' = \frac{x \left(- e^{x^{2} + y^{2}} + 2 \cos{\left(x^{2} \right)} \cos{\left(y^{2} \right)}\right)}{y \left(e^{x^{2} + y^{2}} + 2 \sin{\left(x^{2} \right)} \sin{\left(y^{2} \right)}\right)}