Erin Stafford

2023-03-23

What is the derivative of $\frac{x+1}{y}$?

pistuiescvzeb

Beginner2023-03-24Added 10 answers

Utilize the chain rule and the quotient rule.(all implicit differentiation uses the chain rule.)

$\frac{d}{dx}\left(\frac{x+1}{y}\right)=\frac{\left(1\right)y-(x+1)\frac{dy}{dx}}{{y}^{2}}$

There's not much more we can do without the rest of the equation relating $x$ and $y$.

We could rewrite a bit, to get:

$=\frac{y-(x+1)\frac{dy}{dx}}{{y}^{2}}$

or

$=\frac{1}{y}-\frac{x+1}{{y}^{2}}\frac{dy}{dx}$

$\frac{d}{dx}\left(\frac{x+1}{y}\right)=\frac{\left(1\right)y-(x+1)\frac{dy}{dx}}{{y}^{2}}$

There's not much more we can do without the rest of the equation relating $x$ and $y$.

We could rewrite a bit, to get:

$=\frac{y-(x+1)\frac{dy}{dx}}{{y}^{2}}$

or

$=\frac{1}{y}-\frac{x+1}{{y}^{2}}\frac{dy}{dx}$

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