Question

if $f(x)=\frac{5x^{5}-6x^{4}-7x^{3}}{x^{4}}$, find $f(x)$

Explanation:

Step1: Simplify the function

First, simplify $f(x)=\frac{5x^{5}-0x^{4}-7x^{3}}{x^{4}}=\frac{5x^{5}-7x^{3}}{x^{4}} = 5x - \frac{7}{x}$.

Step2: Apply derivative rules

The derivative of $5x$ is $5$ (using the power - rule $\frac{d}{dx}(ax)=a$ where $a = 5$), and the derivative of $-\frac{7}{x}=-7x^{-1}$ is $7x^{-2}$ (using the power - rule $\frac{d}{dx}(ax^{n})=nax^{n - 1}$, here $a=-7$ and $n=-1$).

Answer:

$5+\frac{7}{x^{2}}$