OK i get most of it now. Implicit differentiation is the key.
I still cant quite understand how -2(y')^2 differentiates to -4y'y''
Hi There,
Below is an answer from one of my assignments. I am trying to understand the answer however i am stuck on the parts as listed below.
I have been through my books and online a thousand time but i just cant get my head around this. Your help will be very much appreciated!
Rearrange to the form
y′ = 2x2 − y2 (1)
and evaluate at x = 0:
y′(0) = −y2(0) = −4 .
Differentiate (1): How does this differentiate?
y′′ = 4x − 2yy′ (2)
from where
y′′(0) = −2y(0)y′(0) = 16 .
Now differentiate (2):
y′′′ = 4 − 2(y′)2 − 2yy′′ (3) And this one also?
from where
y′′′(0) = 4 − 2(y′(0))2 − 2y(0)y′′(0) = −92 .
Differentiate (3):
y′′′′ = −4y′y′′ − 2y′y′′ − 2yy′′′ (4) And again?