Question

differentiate $y = \frac{12}{x^{2}}$

Explanation:

Step1: Rewrite the function

Rewrite \( y=\frac{12}{x^{2}} \) as \( y = 12x^{-2} \).

Step2: Apply the power rule

The power rule for differentiation is \( \frac{d}{dx}(x^{n})=nx^{n - 1} \).
For \( y = 12x^{-2} \), using the constant - multiple rule \( \frac{d}{dx}(cf(x))=c\frac{d}{dx}(f(x)) \) (where \( c = 12 \) and \( f(x)=x^{-2} \)), we have \( y'=12\times(-2)x^{-2-1} \).

Step3: Simplify the expression

\( y'=-24x^{-3} \).

Answer:

\( y'=-24x^{-3} \) (the third option).