Implicit Di erentiation Partial Solution Guide - ? Implicit Di erentiation Partial Solution Guide

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    02-Sep-2018

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  • Implicit Differentiation Partial Solution Guide

    In this guide, I will do one problem to help you.

    7. Find the derivative y(x) implicitly. Note: y(x) is equivalent to saying dydx .

    xy 4y2 = 12

    ddx [xy 4y2] = ddx [12]

    12(xy)

    1/2(x dydx + y) 8ydydx = 0

    x2xy

    dydx +

    y2xy 8y

    dydx = 0

    x2xy

    dydx 8y

    dydx =

    y2xy (

    x2xy 8y)

    dydx =

    y2xy

    dydx =

    yxxy

    x2xy8y

    dydx =

    yxxy

    x16yxy2xy

    dydx =

    2yxxy(x16yxy)

    This is good enough. Dont you just love the Chain Rule?

    Note: As I keep saying in these things, it looks complicated and, yes, it is tedious, but if youjust look at each piece as small parts and work with them that way and put them together,then this will be manageable. If you freak yourself out by looking at this, then you willnot succeed. Its all about understanding the basics and applying basic principles to morecomplicated things.

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