Question

if $f(x)=\frac{-8x^{5}+4x^{4}+5x^{3}}{x^{4}}$. find $f(x)$. $f(x)=$ submit answer next item

Explanation:

Step1: Simplify the function

First, simplify $f(x)=\frac{-8x^{5}+4x^{4}+5x^{3}}{x^{4}}$ using the rule of dividing powers with the same base $\frac{a^{m}}{a^{n}}=a^{m - n}$.
$f(x)=-8x^{5 - 4}+4x^{4 - 4}+5x^{3 - 4}=-8x + 4+5x^{-1}$

Step2: Differentiate term - by - term

Use the power rule for differentiation $\frac{d}{dx}(ax^{n})=nax^{n - 1}$.
For the first term $-8x$, its derivative is $\frac{d}{dx}(-8x)=-8$.
For the second term $4$ (a constant), its derivative is $\frac{d}{dx}(4)=0$.
For the third term $5x^{-1}$, its derivative is $\frac{d}{dx}(5x^{-1})=- 5x^{-2}$.

Step3: Combine the derivatives

$f'(x)=-8+0 - 5x^{-2}=-8-\frac{5}{x^{2}}$

Answer:

$-8-\frac{5}{x^{2}}$