How do you implicitly differentiate # 2y^2 - 3x^2y + x = 4y#?

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Answer 1 · 2016-03-07T18:02:47

You can do it like this:

#2y^2-3x^2y+x=4y#

Differentiate both sides implicitly:

#D(2y^2-3x^(2)y+x)=D(4y)#

#:.4y.y'-(3x^(2).y'+y.6x)+1=4y'#

#:.4y.y'-3x^2.y'-6xy+1=4y'#

#:.4y.y'-4y'-3x^2.y'=6xy-1#

#:.y'(4y-4-3x^2)=(6xy-1)#

#:.y'=((6xy-1))/((4y-4-3x^2))#