Question

hw_2.1_basic derivative rules
due sunday by 11:59pm points 100.05 submitting an ex
hw_2.1_basic derivative rules

1. submit answer practice similar

attempt 1: 10 attempts remaining.
if $f(x)=\frac{15}{x^{6}}$, find $f(x)$.
answer:
submit answer next item

Explanation:

Step1: Rewrite the function

Rewrite $f(x)=\frac{15}{x^{6}}$ as $f(x)=15x^{- 6}$ using the rule $\frac{1}{a^{n}}=a^{-n}$.

Step2: Apply the power - rule for derivatives

The power - rule states that if $y = ax^{n}$, then $y'=anx^{n - 1}$. For $f(x)=15x^{-6}$, where $a = 15$ and $n=-6$, we have $f'(x)=15\times(-6)x^{-6 - 1}$.

Step3: Simplify the result

$f'(x)=-90x^{-7}=-\frac{90}{x^{7}}$.

Answer:

$-\frac{90}{x^{7}}$