1. ## Please show me the steps to differentiate this function

Hello,

Could someone please show me the steps you would follow to differentiate the following function:

xy^2 - 2y = x + 5

Thanks,

Alex

2. Originally Posted by alex95
Hello,

Could someone please show me the steps you would follow to differentiate the following function:

xy^2 - 2y = x + 5

Thanks,

Alex
Do you know implicit differentiation? Or if you are in calc 3 you can use another method. Where are you in your Calculus?

3. Calc 1

Thanks,

Alex

4. Originally Posted by alex95
Calc 1

Thanks,

Alex
$\displaystyle xy^2 - 2y = x + 5$

$\displaystyle \text{product rule}1\cdot y^2+x2yy')-2y'=1$

Isolate y'

$\displaystyle \displaystyle 2xyy'-2y'=1-y^2\Rightarrow y'(2xy-2)=1-y^2\Rightarrow y'=\frac{1-y^2}{2xy-2}$