Question

question given the function f(x) = 3/sqrt(x), find f(x). express your answer in radical form without using negative exponents, simplifying all fractions. answer attempt 1 out of 2 f(x) = submit answer watch video show examples

Explanation:

Step1: Rewrite the function

Rewrite $f(x)=\frac{3}{\sqrt{x^3}}$ as $f(x)=3x^{-\frac{3}{2}}$.

Step2: Apply power - rule for differentiation

The power - rule states that if $y = ax^n$, then $y'=anx^{n - 1}$. For $f(x)=3x^{-\frac{3}{2}}$, we have $a = 3$ and $n=-\frac{3}{2}$. So $f'(x)=3\times(-\frac{3}{2})x^{-\frac{3}{2}-1}$.

Step3: Simplify the exponent and coefficient

$f'(x)=-\frac{9}{2}x^{-\frac{5}{2}}$.

Step4: Rewrite without negative exponents

$f'(x)=-\frac{9}{2x^{\frac{5}{2}}}=-\frac{9}{2\sqrt{x^5}}$.

Answer:

$-\frac{9}{2\sqrt{x^5}}$