Use implicit differentiation where $LaTeX: \displaystyle y$ is a function of $LaTeX: \displaystyle x$ to find the derivative of $LaTeX: \displaystyle 4 e^{x} e^{y} - 4 \log{\left(y \right)} \cos{\left(x^{3} \right)}=-49$

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