Question

question 9 - 1 point find the derivative of $f(x)=-\frac{4}{3x^{4}}$. provide your answer below: $f(x)=square$

Explanation:

Step1: Recall power - rule for derivatives

The power - rule states that if $y = ax^n$, then $y^\prime=anx^{n - 1}$, where $a$ is a constant and $n$ is a real number. For the function $f(x)=-\frac{4}{3}x^{4}$, we have $a =-\frac{4}{3}$ and $n = 4$.

Step2: Apply the power - rule

$f^\prime(x)=-\frac{4}{3}\times4x^{4 - 1}$.

Step3: Simplify the expression

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

Answer:

$-\frac{16}{3}x^{3}$