I know this has been asked in many forms. But still confused. I am re-learning differential equations and I was working on Verifying solutions.
Is $g(x) = (\frac{\sqrt 3x^2}{2})$ a solution to $\displaystyle g'(x) = \frac{3x}{4g(x)}$
When plugging in.. I get confused with
$\displaystyle\frac{3x}{4\frac{\sqrt 3x^2}{2}}$
If you have $\frac ab$ ÷ $\frac pq$ you $\frac ab$ x $\frac qp$ ...I know why
But what do you do when $\displaystyle\frac a{b({\frac pq})}$ ...especially for such cases.
$$ \dfrac{a}{\frac{bp}{q}} = a \cdot \dfrac{q}{bp} $$
This is because $a ÷ \dfrac{b}{c}=a \cdot \dfrac{c}{b}$. You can get more information here.