find f(x) for the given function. f(x)=6/(3 + x)

Explanation:

Step1: Rewrite the function

Rewrite $f(x)=\frac{6}{3 + x}$ as $f(x)=6(3 + x)^{-1}$.

Step2: Apply the power - rule and chain - rule

The power - rule states that if $y = u^n$, then $y^\prime=nu^{n - 1}u^\prime$. Here $n=-1$ and $u = 3 + x$, so $u^\prime=1$. $f^\prime(x)=6\times(-1)\times(3 + x)^{-2}\times1$.

Step3: Simplify the result

$f^\prime(x)=-\frac{6}{(3 + x)^2}$.

Answer:

$f^\prime(x)=-\frac{6}{(3 + x)^2}$