00:03
We are trying to find the derivative of this equation, finding d, y, dx.
00:09
And as soon as i look at this, i notice i have to use the power rule on the left -hand side.
00:15
I'm going to have to use the chain rule because of the variable expressions inside the parentheses.
00:21
But i'm also going to have to use the product rule as i'm doing my chain rule because of the 3xy.
00:26
And that's just a lot of rules all at once.
00:29
So me personally, i would rather square this binomial and then, deal with each of the terms individually.
00:36
So that's what i'm going to do first.
00:37
I'm going to square this using the squaring the binomial rule.
00:41
So that becomes 9x squared, y squared, plus 42x, y, plus 49 equals the 6y.
00:56
And now when i go to do my derivative of the individual terms, yes, i'll have the product rule twice, but again, i think that's going to be better than what we would have had dealing with it as it was originally written.
01:09
So with the product rule, i'm going to treat the 9x squared as one function, y squared as the other.
01:15
So product rule is first function, 9x squared, times the derivative of the second, which will be 2 times y, times d, y, dx, or y prime...