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Section 3.3 : Differentiation Formulas

12. Find the derivative of \(\displaystyle f\left( y \right) = \frac{{{y^5} - 5{y^3} + 2y}}{{{y^3}}}\) .

Show Solution

There isn’t much to do here other than take the derivative using the rules we discussed in this section.

Remember that in order to do this derivative we’ll first need to divide the function out and simplify before we take the derivative. Here is the rewritten function.

\[f\left( y \right) = \frac{{{y^5}}}{{{y^3}}} - \frac{{5{y^3}}}{{{y^3}}} + \frac{{2y}}{{{y^3}}} = {y^2} - 5 + 2{y^{ - 2}}\]

The derivative is,

\[\require{bbox} \bbox[2pt,border:1px solid black]{{f'\left( y \right) = 2y - 4{y^{ - 3}}}}\]