(a) If $f(x)=x^{4}+5 x$, find $f^{\prime}(x)$ \[ f^{\prime}(x)= \]

Step 1 ：Given the function \(f(x) = x^4 + 5x\), we want to find its derivative \(f'(x)\).

Step 2 ：Using the power rule for differentiation, we have \(f'(x) = 4x^3 + 5\).

Step 3 ：\(\boxed{f'(x) = 4x^3 + 5}\)