Question

question 14 · 1 point
find $\frac{d}{dx}left(\frac{3}{x^{7}}
ight)$.
provide your answer below:
$\frac{d}{dx}left(\frac{3}{x^{7}}
ight)=square$

Explanation:

Step1: Rewrite the function

Rewrite $\frac{3}{x^{7}}$ as $3x^{-7}$ using the rule $\frac{1}{x^{n}}=x^{-n}$.

Step2: Apply the power - rule for differentiation

The power - rule states that if $y = ax^{n}$, then $\frac{dy}{dx}=anx^{n - 1}$. Here $a = 3$ and $n=-7$. So, $\frac{d}{dx}(3x^{-7})=3\times(-7)x^{-7 - 1}$.

Step3: Simplify the result

$3\times(-7)x^{-7 - 1}=-21x^{-8}=-\frac{21}{x^{8}}$.

Answer:

$-\frac{21}{x^{8}}$