\\frac{d}{dx}\\left(\\frac{1}{x^{12}}\\right)=\\square
\\frac{d}{dx}\\left(\\frac{1}{x^{12}}\\right)=\\square
Answer
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:
$-\frac{12}{x^{13}}$