Question

find $\frac{dy}{dx}$ for $y = \frac{1}{x^{14}}$. $\frac{dy}{dx}=square$

Explanation:

Step1: Rewrite the function

Rewrite $y = \frac{1}{x^{14}}$ as $y=x^{- 14}$ using the rule $\frac{1}{a^n}=a^{-n}$.

Step2: Apply power - rule for differentiation

The power - rule states that if $y = x^n$, then $\frac{dy}{dx}=nx^{n - 1}$. For $y=x^{-14}$, we have $n=-14$. So, $\frac{dy}{dx}=-14x^{-14 - 1}$.

Step3: Simplify the result

$-14x^{-14 - 1}=-14x^{-15}=-\frac{14}{x^{15}}$.

Answer:

$-\frac{14}{x^{15}}$