Question

\frac{d}{dx}\left(\frac{1}{x^{12}}\
ight)=\square

Explanation:

Step1: Rewrite the function

Rewrite $\frac{1}{x^{12}}$ as $x^{-12}$.

Step2: Apply the power rule

The power rule for differentiation is $\frac{d}{dx}(x^n)=nx^{n - 1}$.
For $y = x^{-12}$, using the power rule:
$$\frac{d}{dx}(x^{-12})=-12x^{-12 - 1}$$

Step3: Simplify the result

Simplify $-12x^{-13}$ to $-\frac{12}{x^{13}}$.

Answer:

$-\frac{12}{x^{13}}$