Question

find the derivative of the following function by first simplifying the expression.
f(w)=\frac{6w^{8}-7w^{3}}{5w^{3}}
f(w)=square

Explanation:

Step1: Simplify the function

Separate the fraction: $f(w)=\frac{6w^{8}}{5w^{3}}-\frac{7w^{3}}{5w^{3}}=\frac{6}{5}w^{5}-\frac{7}{5}$

Step2: Apply power - rule for derivatives

The derivative of $ax^{n}$ is $nax^{n - 1}$. For $y=\frac{6}{5}w^{5}-\frac{7}{5}$, the derivative of $\frac{6}{5}w^{5}$ is $5\times\frac{6}{5}w^{4}=6w^{4}$, and the derivative of the constant $-\frac{7}{5}$ is 0.

Answer:

$6w^{4}$