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

Explanation:

Step1: Simplify the function

First, divide each term in the numerator by (7w): [ \begin{align*} f(w)&=\frac{5w^{5}-3w}{7w}\ &=\frac{5w^{5}}{7w}-\frac{3w}{7w}\ &=\frac{5}{7}w^{4}-\frac{3}{7} \end{align*} ]

Step2: Apply the power - rule for differentiation

The power - rule states that if (y = ax^{n}), then (y^\prime=anx^{n - 1}), and the derivative of a constant (C) is (0). For (y=\frac{5}{7}w^{4}-\frac{3}{7}), the derivative of (\frac{5}{7}w^{4}) is (\frac{5}{7}\times4w^{4 - 1}=\frac{20}{7}w^{3}), and the derivative of (-\frac{3}{7}) (a constant) is (0).

Answer:

(\frac{20}{7}w^{3})