Question

(d) if $y = \frac{11}{x^{3}}$, find $\frac{dy}{dx}$.
$\frac{dy}{dx}=square$

Explanation:

Step1: Rewrite the function

Rewrite $y = \frac{11}{x^{3}}$ as $y = 11x^{-3}$ using the rule $\frac{1}{a^{n}}=a^{-n}$.

Step2: Apply the power - rule for differentiation

The power - rule states that if $y = ax^{n}$, then $\frac{dy}{dx}=anx^{n - 1}$. Here, $a = 11$ and $n=-3$. So, $\frac{dy}{dx}=11\times(-3)x^{-3 - 1}$.

Step3: Simplify the result

$\frac{dy}{dx}=-33x^{-4}=-\frac{33}{x^{4}}$.

Answer:

$-\frac{33}{x^{4}}$