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tmagloire1
 one year ago
Can anyone help me on this problem regarding implicit differentiation? Thanks
http://prntscr.com/7u700y
tmagloire1
 one year ago
Can anyone help me on this problem regarding implicit differentiation? Thanks http://prntscr.com/7u700y

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DanJS
 one year ago
Best ResponseYou've already chosen the best response.3when differentiating y, remember to use the chain rule...

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3For example, \[\frac{ d }{ dx }[y^3] = \frac{ d }{ dy }[y^3]*\frac{ dy }{ dx }\]

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3Basic chain rule for this \[\frac{ d }{ dx } = \frac{ d }{ dy }*\frac{ dy }{ dx }\]

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3Following the above example, \[\frac{ d }{ dx }[y^3] = 3y^2*\frac{ dy }{ dx }\]

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3Do that for the y terms, and differentiate the x terms normally, then solve for dy/dx

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0Okay I'll try it and tell you what I get.

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0Okay I am actually still very confused. Am i supposed to find the second derivative of 5x^2 + y4 = −9 and then use implicit differentiation?

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3Yes you want to find the second derivative of the given thing with respect to X, but to take the derivative w.r.t. X of the Y term, you have to use that chain rule... here ill type it out

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3\[\frac{ d }{ dx }[5x^2]+\frac{ d }{ dx }y^4 = \frac{ d }{ dx }[9]\] \[\frac{ d }{ dx }[5x^2]+\frac{ d }{ dy }y^4*\frac{ dy }{ dx } = \frac{ d }{ dx }[9]\]

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3now take derivative of y term with respect to y like normal, but you have to put the y' on there too from the chain rule.

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3\[\frac{ d }{ dx }[5x^2]+\frac{ d }{ dy }y^4*\frac{ dy }{ dx } = \frac{ d }{ dx }[9]\] \[10x^2+4y^3*\frac{ dy }{ dx } = 0\]

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3Solve that for dy/dx and that is your first derivative...

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3Or just remember, if you are taking the derivative of a Y term, tag on a dy/dx next to it ...basically

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0Okay for the first derivative I got : dy/dx= 10x^2 / 4y^3

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0And then take the derivative again?

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3So you get, \[\frac{ dy }{ dx } = \frac{ 10x^2 }{ 4y^3 }\] right

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3This time you need the product or the quotient rule and the chain rule...

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3I can start typing it out...

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0Im using the quotient rule

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3\[\frac{ d }{ dx }\frac{ dy }{ dx } = \frac{ d^2y }{ dx^2 }\] k, ill start typing it

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0I got : 80xy^3 +120x^2y^2 / (4y^3)^2

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3\[\frac{ d^2y }{ dx^2 } = \frac{ d }{ dx}\frac{ 5x^2 }{ 2y^3 }\]

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0Oh I think I took the derivative of the wrong thing?

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0So it would be 20 when you plug in x and y

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3\[\frac{ d^2y }{ dx^2 }=\frac{ 2y^2*10x  [5x*6y^2*\frac{ dy }{ dx } ]}{ 4y^6 }\]

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3That is the quotient rule , using the chain rule on the y term in the numorator.

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0So am I supposed to plug in x and y into which equation?

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3yes, but notice the second derivative has a term of the first derivative in the numerator... but you know what dy/dx is , so sub that in first

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3\[\frac{ dy }{ dx } = \frac{ 5x^2 }{ 2y^3 }\] reduced fraction... Sub that in for dyy/dx in the second derivative then plug in the x and y and solve...

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3Less writing overall if you want to use y' and y'' instead of dy/dx things

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3goodluck, i dont want to calculate it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\large \color{blue}{\checkmark}\]

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0Thanks for all the help!

DanJS
 one year ago
Best ResponseYou've already chosen the best response.3yw, just get that Leibanitz notation dy/dx crap down, it makes the chain rule and this stuff easier i think .. goodluck

tmagloire1
 one year ago
Best ResponseYou've already chosen the best response.0Okay I will try using it more.
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