Question

differentiate.
y = \frac{x}{9}-\frac{9}{x}
\frac{d}{dx}(\frac{x}{9}-\frac{9}{x}) = \square

Explanation:

Step1: Differentiate term - by - term

$\frac{d}{dx}(\frac{x}{9})-\frac{d}{dx}(\frac{9}{x})$

Step2: Differentiate $\frac{x}{9}$

$\frac{1}{9}\frac{d}{dx}(x)=\frac{1}{9}$

Step3: Differentiate $\frac{9}{x}=9x^{-1}$

$9\frac{d}{dx}(x^{-1})=- 9x^{-2}=-\frac{9}{x^{2}}$

Step4: Combine results

$\frac{1}{9}+\frac{9}{x^{2}}$

Answer:

$\frac{1}{9}+\frac{9}{x^{2}}$