QuestionUse logarithmic differentiation to differentiate each function with respect to $x$. You do not need to simplify or substitute for $y$. $$y=\frac{\left(x^{2}+4\right)^{3}}{\left(2 x^{4}-1\right)^{5} \cdot\left(4 x^{9}+5\right)^{6}}$$ A) $\frac{d y}{d x}=y\left(\frac{6 x}{x^{2}+4}-\frac{160 x^{3}}{2 x^{4}-1}-\frac{864 x^{8}}{4 x^{9}+5}\right)$ B) $\frac{d y}{d x}=y\left(\frac{18 x}{x^{2}+4}-\frac{80 x^{3}}{2 x^{4}-1}+\frac{432 x^{8}}{4 x^{9}+5}\right)$ C) $\frac{d y}{d x}=y\left(\frac{6 x}{x^{2}+4}-\frac{40 x^{3}}{2 x^{4}-1}+\frac{864 x^{8}}{4 x^{9}+5}\right)$ D) $\frac{d y}{d x}=y\left(\frac{6 x}{x^{2}+4}-\frac{40 x^{3}}{2 x^{4}-1}-\frac{216 x^{8}}{4 x^{9}+5}\right)$