what is the value of $\frac{d}{dx}left(\frac{1}{x}\right)$ at $x = 6$? you might need: calculator

Explanation:

Step1: Recall power - rule for differentiation

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

Step2: Differentiate $x^{-1}$

Using the power - rule, if $y=x^{-1}$, then $\frac{d}{dx}(x^{-1})=-1\times x^{-1 - 1}=-x^{-2}=-\frac{1}{x^{2}}$.

Step3: Evaluate at $x = 6$

Substitute $x = 6$ into $-\frac{1}{x^{2}}$. We get $-\frac{1}{6^{2}}=-\frac{1}{36}$.

Answer:

$-\frac{1}{36}$