homework5: problem 34 (1 point) if (f(x)=sqrt{23x}), find (f(x)). (f(x)=)

Explanation:

Step1: Rewrite the function

Rewrite $f(x)=\sqrt{23x}$ as $f(x)=(23x)^{\frac{1}{2}}$.

Step2: Apply the power - rule for differentiation

The power - rule states that if $y = ax^n$, then $y'=anx^{n - 1}$. Here $a = 23^{\frac{1}{2}}$ and $n=\frac{1}{2}$. So $f'(x)=\frac{1}{2}(23x)^{-\frac{1}{2}}\times23$.

Step3: Simplify the result

$f'(x)=\frac{23}{2\sqrt{23x}}$.

Answer:

$\frac{23}{2\sqrt{23x}}$