(
(a) Let $f(x)=\sqrt{9+8x^3}$. Find $f^{\prime }(x)$.
$$f^{\prime }(x)=$$
(b) Let $f(x)=e^{\sqrt{9+8x^3}}$. Find $f^{\prime }(x)$.
$$f^{\prime }(x)=$$

Step 1 ：Identify the outer function as $\sqrt{u}$ and its derivative as $\frac{1}{2\sqrt{u}}$

Step 2 ：Identify the inner function as $9+8x^3$ and its derivative as $24x^2$

Step 3 ：Apply the chain rule to find the derivative of $f(x)=\sqrt{9+8x^3}$, which is $f^{\prime }(x)=\frac{1}{2\sqrt{9+8x^3}}\cdot 24x^2$

Step 4 ：Simplify the derivative to get $f^{\prime }(x)=\frac{12x^2}{\sqrt{9+8x^3}}$

Step 5 ：$\boxed{{\displaystyle f^{\prime }(x)=\frac{12x^2}{\sqrt{9+8x^3}}}}$ is the derivative of $f(x)=\sqrt{9+8x^3}$

Step 6 ：Identify the outer function as $e^u$ and its derivative as $e^u$

Step 7 ：Identify the inner function as $\sqrt{9+8x^3}$ and its derivative as $\frac{12x^2}{\sqrt{9+8x^3}}$

Step 8 ：Apply the chain rule to find the derivative of $f(x)=e^{\sqrt{9+8x^3}}$, which is $f^{\prime }(x)=e^{\sqrt{9+8x^3}}\cdot \frac{12x^2}{\sqrt{9+8x^3}}$

Step 9 ：Simplify the derivative to get $f^{\prime }(x)=\frac{12x^2{e}^{\sqrt{9+8x^3}}}{\sqrt{9+8x^3}}$

Step 10 ：$\boxed{{\displaystyle f^{\prime }(x)=\frac{12x^2{e}^{\sqrt{9+8x^3}}}{\sqrt{9+8x^3}}}}$ is the derivative of $f(x)=e^{\sqrt{9+8x^3}}$