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