Question

question find the derivative of f(x)=\frac{-4x^{6}+4x^{5}-3x^{3}}{3x^{2}}. provide your answer below: f(x)=□

Explanation:

Step1: Simplify the function

First, simplify $f(x)=\frac{-4x^{6}+4x^{5}-3x^{3}}{3x^{2}}=-\frac{4}{3}x^{4}+\frac{4}{3}x^{3}-x$.

Step2: Apply power - rule for derivatives

The power - rule states that if $y = ax^{n}$, then $y^\prime=anx^{n - 1}$.
For $y =-\frac{4}{3}x^{4}$, $y^\prime=-\frac{4}{3}\times4x^{3}=-\frac{16}{3}x^{3}$.
For $y=\frac{4}{3}x^{3}$, $y^\prime=\frac{4}{3}\times3x^{2}=4x^{2}$.
For $y = - x$, $y^\prime=-1$.

Step3: Combine the derivatives

$f^\prime(x)=-\frac{16}{3}x^{3}+4x^{2}-1$.

Answer:

$-\frac{16}{3}x^{3}+4x^{2}-1$