Please show me the steps to differentiate this function

**alex95** · February 1st 2011, 11:37 AM

Hello,

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

xy^2 - 2y = x + 5

Thanks,

Alex

**dwsmith** · February 1st 2011, 11:39 AM

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?

**alex95** · February 1st 2011, 11:44 AM

Calc 1

Thanks,

Alex

**dwsmith** · February 1st 2011, 11:50 AM

Originally Posted by alex95

Calc 1

Thanks,

Alex

$xy^2 - 2y = x + 5$

$\text{product rule}<img src=$ 1\cdot y^2+x2yy')-2y'=1" alt="\text{product rule}

1\cdot y^2+x2yy')-2y'=1" />

Isolate y'

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

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