Use implicit differentiation where LaTeX: \displaystyle y is a function of LaTeX: \displaystyle x to find the derivative of LaTeX: \displaystyle - 5 e^{y^{2}} \cos{\left(x^{2} \right)} + 5 \log{\left(x \right)} \cos{\left(y^{2} \right)}=35

Taking the derivative of both sides using implicit differentiation gives: LaTeX: 10 x e^{y^{2}} \sin{\left(x^{2} \right)} - 10 y y' e^{y^{2}} \cos{\left(x^{2} \right)} - 10 y y' \log{\left(x \right)} \sin{\left(y^{2} \right)} + \frac{5 \cos{\left(y^{2} \right)}}{x} = 0 Solving for LaTeX: \displaystyle y' gives LaTeX: \displaystyle y' = \frac{x^{2} e^{y^{2}} \sin{\left(x^{2} \right)} + \frac{\cos{\left(y^{2} \right)}}{2}}{x y \left(e^{y^{2}} \cos{\left(x^{2} \right)} + \log{\left(x \right)} \sin{\left(y^{2} \right)}\right)}