Use implicit differentiation where LaTeX: \displaystyle y is a function of LaTeX: \displaystyle x to find the derivative of LaTeX: \displaystyle - 8 \sqrt{7} \sqrt{y} \cos{\left(x \right)} - 6 y \log{\left(x \right)}=-26

Taking the derivative of both sides using implicit differentiation gives: LaTeX: 8 \sqrt{7} \sqrt{y} \sin{\left(x \right)} - 6 y' \log{\left(x \right)} - \frac{4 \sqrt{7} y' \cos{\left(x \right)}}{\sqrt{y}} - \frac{6 y}{x} = 0 Solving for LaTeX: \displaystyle y' gives LaTeX: \displaystyle y' = \frac{4 \sqrt{7} x y \sin{\left(x \right)} - 3 y^{\frac{3}{2}}}{x \left(3 \sqrt{y} \log{\left(x \right)} + 2 \sqrt{7} \cos{\left(x \right)}\right)}