Find the derivative of the following function and simplify_the answers as much as possible: f(x)=\frac{\left(2 e^{\sqrt{x}}+3\right) \log _{2}\left(2 e^{\sqrt{x}}+3\right)}{\left.\log _{3}\left(9^{\left(2 e^{\sqrt{x}}+3\right.}\right)\right)} \frac{\mathrm{d} f}{\mathrm{~d} x}=\frac{\sqrt{x}}{\left.2 e^{\sqrt{x}}+3\right)} \text { b) } \frac{\mathrm{d}

f}{\mathrm{~d} x}=\frac{1}{\left(2 e^{\sqrt{x}}+3\right) \sqrt{x}} \text { c) None of the answers given here. } \text { d) } \frac{\mathrm{d} f}{\mathrm{~d} x}=\frac{1}{\ln 4\left(2 e^{\sqrt{x}}+3\right) \sqrt{x}} \frac{\mathrm{d} f}{\mathrm{~d} x}=\frac{1}{\ln 2\left(2 e^{\sqrt{x}}+3\right) \sqrt{x}} \text { g) } \frac{\mathrm{d} f}{\mathrm{~d} x}=\frac{\sqrt{x}}{\ln 4\left(2 e^{\sqrt{x}}+3\right)}