Use implicit differentiation where $LaTeX: \displaystyle y$ is a function of $LaTeX: \displaystyle x$ to find the derivative of $LaTeX: \displaystyle 4 y e^{x^{3}} + 7 \log{\left(y \right)} \sin{\left(x \right)}=36$

Taking the derivative of both sides using implicit differentiation gives: $LaTeX: 12 x^{2} y e^{x^{3}} + 4 y' e^{x^{3}} + 7 \log{\left(y \right)} \cos{\left(x \right)} + \frac{7 y' \sin{\left(x \right)}}{y} = 0$ Solving for $LaTeX: \displaystyle y'$ gives $LaTeX: \displaystyle y' = - \frac{y \left(12 x^{2} y e^{x^{3}} + 7 \log{\left(y \right)} \cos{\left(x \right)}\right)}{4 y e^{x^{3}} + 7 \sin{\left(x \right)}}$