Use implicit differentiation where $LaTeX: \displaystyle y$ is a function of $LaTeX: \displaystyle x$ to find the derivative of $LaTeX: \displaystyle 7 e^{x^{3}} \cos{\left(y \right)} - 5 \sin{\left(x \right)} \sin{\left(y \right)}=-41$

Taking the derivative of both sides using implicit differentiation gives: $LaTeX: 21 x^{2} e^{x^{3}} \cos{\left(y \right)} - 7 y' e^{x^{3}} \sin{\left(y \right)} - 5 y' \sin{\left(x \right)} \cos{\left(y \right)} - 5 \sin{\left(y \right)} \cos{\left(x \right)} = 0$ Solving for $LaTeX: \displaystyle y'$ gives $LaTeX: \displaystyle y' = \frac{21 x^{2} e^{x^{3}} \cos{\left(y \right)} - 5 \sin{\left(y \right)} \cos{\left(x \right)}}{7 e^{x^{3}} \sin{\left(y \right)} + 5 \sin{\left(x \right)} \cos{\left(y \right)}}$