I need the y′′ by implicit differentiation 2x^3+5y^3=2

vrteclh

vrteclh

Open question

2022-08-14

I need to find y by implicit differentiation : 2 x 3 + 5 y 3 = 2

Answer & Explanation

Pasrbekwp

Pasrbekwp

Beginner2022-08-15Added 10 answers

Take the derivative:
6 x 2 + 15 y 2 y = 0 (applied chin rule to y)
y = 6 x 2 15 y 2
Take the derivative one more time:
12 x ( 15 y 2 ) ( 30 y y ( 6 x 2 ) ) ( 15 y 2 ) 2 now replace y by y = 6 x 2 15 y 2
traquealwm

traquealwm

Beginner2022-08-16Added 4 answers

Differentiate twice below,
6 x 2 + 15 y 2 y = 0
12 x + 30 y y + 15 y 2 y = 0
Then, isolate y ,
y = 1 15 y 2 ( 12 x + 30 y y )
= 4 5 y 2 ( x 5 x 2 y )
where y = 2 x 2 5 y 2 is used.

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