find $\frac{dy}{dx}$. $y = x^{-12}$ $\frac{dy}{dx}=square$

Explanation:

Step1: Recall power - rule of differentiation

The power - rule states that if $y = x^n$, then $\frac{dy}{dx}=nx^{n - 1}$.

Step2: Identify the value of n

Here, $n=-12$.

Step3: Apply the power - rule

Substitute $n = - 12$ into the power - rule formula: $\frac{dy}{dx}=-12x^{-12 - 1}$.

Step4: Simplify the expression

$\frac{dy}{dx}=-12x^{-13}=-\frac{12}{x^{13}}$.

Answer:

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