Use implicit differentiation where LaTeX: \displaystyle y is a function of LaTeX: \displaystyle x to find the derivative of LaTeX: \displaystyle 8 x^{2} e^{y} + 4 \log{\left(x \right)} \cos{\left(y^{2} \right)}=26

Taking the derivative of both sides using implicit differentiation gives: LaTeX: 8 x^{2} y' e^{y} + 16 x e^{y} - 8 y y' \log{\left(x \right)} \sin{\left(y^{2} \right)} + \frac{4 \cos{\left(y^{2} \right)}}{x} = 0 Solving for LaTeX: \displaystyle y' gives LaTeX: \displaystyle y' = - \frac{4 x^{2} e^{y} + \cos{\left(y^{2} \right)}}{2 x \left(x^{2} e^{y} - y \log{\left(x \right)} \sin{\left(y^{2} \right)}\right)}