Question

complete parts (a) through (d) below.
(a) if f(x)=6x^9, find f(x).
f(x)=□

Explanation:

Step1: Recall power - rule for differentiation

The power - rule states that if $y = ax^n$, then $y^\prime=anx^{n - 1}$, where $a$ is a constant and $n$ is a real number.

Step2: Identify $a$ and $n$

For the function $f(x)=6x^{9}$, we have $a = 6$ and $n = 9$.

Step3: Apply the power - rule

$f^\prime(x)=6\times9x^{9 - 1}$.

Step4: Simplify the expression

$f^\prime(x)=54x^{8}$.

Answer:

$54x^{8}$