find dy/dx if x^4+x^2x^3-y^5=2x+1
saialapati99:
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Begin with x3 + y3 = 4 . Differentiate both sides of the equation, getting
D ( x3 + y3 ) = D ( 4 ) ,
D ( x3 ) + D ( y3 ) = D ( 4 ) ,
(Remember to use the chain rule on D ( y3 ) .)
3x2 + 3y2 y' = 0 ,
so that (Now solve for y' .)
3y2 y' = - 3x2
D ( x3 + y3 ) = D ( 4 ) ,
D ( x3 ) + D ( y3 ) = D ( 4 ) ,
(Remember to use the chain rule on D ( y3 ) .)
3x2 + 3y2 y' = 0 ,
so that (Now solve for y' .)
3y2 y' = - 3x2
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