find the derivative of the following function by first simplifying the expression. f(w)=(4w^3 - 5w)/3w f(w)=

Answer:

$\frac{8w}{3}-\frac{5}{3}$

Explanation:

Step1: Simplify the function

$f(w)=\frac{4w^{3}-5w}{3w}=\frac{4w^{3}}{3w}-\frac{5w}{3w}=\frac{4}{3}w^{2}-\frac{5}{3}$

Step2: Apply power - rule for derivatives

The power - rule states that if $y = ax^{n}$, then $y^\prime=anx^{n - 1}$. For $y=\frac{4}{3}w^{2}$, $y^\prime=\frac{4}{3}\times2w^{2 - 1}=\frac{8}{3}w$, and for $y =-\frac{5}{3}$ (a constant), $y^\prime = 0$. So $f^\prime(w)=\frac{8}{3}w+0=\frac{8w}{3}-\frac{5}{3}$