00:01
Given this expression in terms of x and y.
00:03
We want to find the second derivative of y with respect to x by using implicit differentiation.
00:11
So i'm going to take the derivative with respect to x, like that.
00:27
And i'll solve for dy dx.
00:44
Okay, now i'm gonna take another derivative.
00:55
18 over 32 is 9 16ths.
01:00
Okay, and we get one over y.
01:06
Minus x over y squared dy dx.
01:14
Okay, i'm gonna substitute in dy dx from what i had before.
01:27
So dy dx is minus nine over 16 times x over y.
01:47
So that's minus nine over 16, one over y, minus 81 over 256.
02:01
Then it's x squared over y cubed.
02:06
We want to write this in terms of y alone, i guess.
02:10
I think that's what that means...