Implicit differentiation

Question

I am currently working on a question which involves me differentiating $$\frac{y}{x}$$

I can't find nothing in books or on the internet about how to deal with this kind of implicit differentiation.

Answer 1

The quotient rule is an equally valid way of going about differentiating your expression. If $u$ and $v$ are functions of $x$, then $$ \dfrac{\text{d}}{\text{d}x} \left( \dfrac{u}{v} \right) = \dfrac{vu'-uv'}{v^2}$$ Let $u=y(x)$ and $v=x$ and your result should fall out rather nicely. ^_^

Answer 2

Use the product rule $(fg)' = f'g + fg'$.

$$\frac{d}{dx}\Big(\frac{y}{x}\Big) = \frac{y'}{x} - \frac{y}{x^2} $$