Question

Find y' if y = x/(x+y)

Answer 1

\[y=\frac{x}{x+y}\\
y'=\frac{\frac{d}{dx}\left[x+y\right]\cdot x-\frac{d}{dx}\left[x\right]\cdot(x+y)}{(x+y)^2}\]
Keep in mind that you're doing implicit differentiation...

Answer 2

Use the quotient rule. \[\frac{ du }{ dv } \frac{ u }{ v } = \frac{ u'v-v'u }{ v^2 }\]Now, substitute\[u = x \]And \[v = x+y\]

Answer 3

I'm familiar with the quotient rule, I'm just iffy on implicit differentiation. Would it be