How do you differentiate 5xy + y^3 = 2x + 3y

braffter92 2022-09-29 Answered
How do you differentiate 5 x y + y 3 = 2 x + 3 y
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Answers (1)

recepiamsb
Answered 2022-09-30 Author has 9 answers
You can use implicit differentiation rememberig that y represents a function of x and needs to be differentiated accordingly;
for example: if you have y 2 you differentiate it to get:
2 y d y d x where you use d y d x to take into account the dependence with x.
In your case you get:
5 y + 5 x d y d x + 3 y 2 d y d x = 2 + 3 d y d x
collect d y d x
d y d x ( 5 x + 3 y 2 - 3 ) = 2 - 5 y
and
d y d x = 2 - 5 y 5 x + 3 y 2 - 3
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