Use implicit differentiation where LaTeX: \displaystyle y is a function of LaTeX: \displaystyle x to find the derivative of LaTeX: \displaystyle 5 x^{2} \log{\left(y \right)} - 6 \sin{\left(x \right)} \sin{\left(y \right)}=-26

Taking the derivative of both sides using implicit differentiation gives: LaTeX: \frac{5 x^{2} y'}{y} + 10 x \log{\left(y \right)} - 6 y' \sin{\left(x \right)} \cos{\left(y \right)} - 6 \sin{\left(y \right)} \cos{\left(x \right)} = 0 Solving for LaTeX: \displaystyle y' gives LaTeX: \displaystyle y' = \frac{2 y \left(- 5 x \log{\left(y \right)} + 3 \sin{\left(y \right)} \cos{\left(x \right)}\right)}{5 x^{2} - 6 y \sin{\left(x \right)} \cos{\left(y \right)}}