Use implicit differentiation where $LaTeX: \displaystyle y$ is a function of $LaTeX: \displaystyle x$ to find the derivative of $LaTeX: \displaystyle 7 x^{3} y^{3} - 4 \log{\left(y \right)} \cos{\left(x^{2} \right)}=42$

Taking the derivative of both sides using implicit differentiation gives: $LaTeX: 21 x^{3} y^{2} y' + 21 x^{2} y^{3} + 8 x \log{\left(y \right)} \sin{\left(x^{2} \right)} - \frac{4 y' \cos{\left(x^{2} \right)}}{y} = 0$ Solving for $LaTeX: \displaystyle y'$ gives $LaTeX: \displaystyle y' = - \frac{x y \left(21 x y^{3} + 8 \log{\left(y \right)} \sin{\left(x^{2} \right)}\right)}{21 x^{3} y^{3} - 4 \cos{\left(x^{2} \right)}}$