Use implicit differentiation where LaTeX: \displaystyle y is a function of LaTeX: \displaystyle x to find the derivative of LaTeX: \displaystyle \sin{\left(x \right)} + \sin{\left(y \right)} \cos{\left(x \right)}=40

Taking the derivative of both sides using implicit differentiation gives: LaTeX: y' \cos{\left(x \right)} \cos{\left(y \right)} - \sin{\left(x \right)} \sin{\left(y \right)} + \cos{\left(x \right)} = 0 Solving for LaTeX: \displaystyle y' gives LaTeX: \displaystyle y' = \tan{\left(x \right)} \tan{\left(y \right)} - \frac{1}{\cos{\left(y \right)}}