Use implicit differentiation where LaTeX: \displaystyle y is a function of LaTeX: \displaystyle x to find the derivative of LaTeX: \displaystyle 7 x y + 7 \log{\left(x \right)} \cos{\left(y \right)}=24

Taking the derivative of both sides using implicit differentiation gives: LaTeX: 7 x y' + 7 y - 7 y' \log{\left(x \right)} \sin{\left(y \right)} + \frac{7 \cos{\left(y \right)}}{x} = 0 Solving for LaTeX: \displaystyle y' gives LaTeX: \displaystyle y' = - \frac{x y + \cos{\left(y \right)}}{x \left(x - \log{\left(x \right)} \sin{\left(y \right)}\right)}