How do you implicitly differentiate x+xy-2x^3 = 2

Dorsheele0p

Dorsheele0p

Answered question

2022-08-12

How do you implicitly differentiate x + x y - 2 x 3 = 2

Answer & Explanation

yassou1v

yassou1v

Beginner2022-08-13Added 14 answers

Let us define f ( x , y ) = x + x y - 2 x 3 = 2
d f d x = d f d y d y d x , and so every time you differentiate ( d f d y ) a part of the function
that has y, you have to multiply by d y d x , the derivative of y with respect to x, for the
overall derivative ( d f d x ) to still be with respect to x (even though you're differentiating y).
d f d x = d ( x ) d x + [ x d y d x + y d ( x ) d x ] - d ( 2 x 3 ) d x = d ( 0 ) d x
(has product rule)
1 + [ x d y d x + y ] - 6 x 2 = 0
Simple algebra from here:
x d y d x = 6 x 2 - 1 - y
d y d x = 6 x 2 - y - 1 x

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