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find dy/dx using implicit differentiation: y= 3xy - 2x^3

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find dy/dx using implicit differentiation: y= 3xy - 2x^3.

asked Feb 28, 2014 in CALCULUS by harvy0496 Apprentice

1 Answer

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y  =  3 x y - 2 x 3

Derivitive each term with respected to x.

d / d( y )d / d x (3 x y )  - d / d 2 x 3 )

d y / d x = 3  d / d x ( x y )  - 2 d / d x 3 )

Apply the power property  d / dx ( x n ) = n  * x n -1 and  prodect property  d / d x ( u v ) = u v ' + v u '

d y / d x = 3 [ x * d y / d x + y * d x / d x ]  - 2   (3 * x 3 -1)

d y / d x = 3 [ x * d y / d x + y * 1 ]  - 2   (3  x 3 -1)

d y / d x = 3 x d y / d x + 3 y   - 2   (3  x 2 )

d y / d x = 3 x d y / d x + 3 y  - 6 x 2 

d y / d x - 3 x d y / d x = 3 y   - 6 x 2  

( 1 - 3 x ) d y / d x = 3 ( y   - 2 x 2 )

 d y / d x  = 3 ( y   - 2 x 2 )  / ( 1 - 3 x )

Therefore   d y / dx = 3 ( y   - 2 x 2 )  / ( 1 - 3 x ).

answered Apr 4, 2014 by friend Mentor

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