Use implicit differentiation where LaTeX: \displaystyle y is a function of LaTeX: \displaystyle x to find the derivative of LaTeX: \displaystyle 9 y^{3} \cos{\left(x \right)} + 2 \sin{\left(x^{2} \right)} \sin{\left(y^{2} \right)}=26

Taking the derivative of both sides using implicit differentiation gives: LaTeX: 4 x \sin{\left(y^{2} \right)} \cos{\left(x^{2} \right)} - 9 y^{3} \sin{\left(x \right)} + 27 y^{2} y' \cos{\left(x \right)} + 4 y y' \sin{\left(x^{2} \right)} \cos{\left(y^{2} \right)} = 0 Solving for LaTeX: \displaystyle y' gives LaTeX: \displaystyle y' = \frac{- 4 x \sin{\left(y^{2} \right)} \cos{\left(x^{2} \right)} + 9 y^{3} \sin{\left(x \right)}}{y \left(27 y \cos{\left(x \right)} + 4 \sin{\left(x^{2} \right)} \cos{\left(y^{2} \right)}\right)}