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posted by  Iam4st8 on 10/6/2008 7:55:45 PM  |  status: Live  

Implicit Differentiation

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Calculus N/A N/A N/A
Question Details:
a couple problems i need help on...

sin(xy)=x2

cos(xy)=x2-y2

Find dy/dx on those ^

and find (dy/dx) for y2-2xy=21 at the point (2,-3)

thanks in advanced!
Tags: Calculus

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posted by ninomunoz on 10/6/2008 8:29:49 PM  |  status: Live
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Response Details:
sin(xy)=x2










________________________________________________________________________________________
cos(xy)=x2-y2









____________________________________________________________________________________
y2-2xy=21









    at (2,-3)
I hope this helps!! Leave me a good rating, please! Thanks.

"Cuando no estas seguro de tus respuestos, o no sabes hacer una problema, solo tienes que pedirme y te voy a ayudar. Si se hacer la problema, te voy a ensenar. 'Mi inteligencia es su inteligencia'".
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posted by Iam4st8 on 10/6/2008 8:50:37 PM  |  status: Live
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Response Details:
If ya dont mind, i have a couple more im running into trouble with..

Find the equation of the tangent line to the function x2+2xy-y2-x=2  at point (1,2)

If sin y=x2, find in terms of x and y.

If x2y=8 then find in terms of x and y at the point (2,4)

Again, Thanks in advanced for all the help.  Working this out is difficult but everyone here helps me learn and make sure im doing it correctly!

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posted by ninomunoz on 10/6/2008 8:55:16 PM  |  status: Live
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Response Details:
Find the equation of the tangent line to the function x2+2xy-y2-x=2  at point (1,2).




            at (1,2)



dy/dx gives you the slope m at any point. Use point-slope formula.
I hope this helps!! Leave me a good rating, please! Thanks.

"Cuando no estas seguro de tus respuestos, o no sabes hacer una problema, solo tienes que pedirme y te voy a ayudar. Si se hacer la problema, te voy a ensenar. 'Mi inteligencia es su inteligencia'".
Oracle
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posted by ninomunoz on 10/6/2008 9:02:59 PM  |  status: Live
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Iam4st8's comment:
"thanks so mucn nino, alot of help tonight!"
Response Details:
If x2y=8 then find in terms of x and y at the point (2,4).






Substitute the dy/dx with y'.. It causes less confusion by removing a fraction. You will replace later.





The derivative of y' is y''.. That is, the derivative of dy/dx is d2y/dx2.







Replace y'' with d2y/dx2. Replace y' with -2y/x.



     at (2,-3)

Substitute values given.
I hope this helps!! Leave me a good rating, please! Thanks.

"Cuando no estas seguro de tus respuestos, o no sabes hacer una problema, solo tienes que pedirme y te voy a ayudar. Si se hacer la problema, te voy a ensenar. 'Mi inteligencia es su inteligencia'".
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