00:01
The theme with implicit differentiation is anytime you differentiate with respect to y, you have to write out the derivative of y.
00:11
So the thing is, is if i ask you for the derivative of x, it's just one.
00:16
But when i ask you for the derivative of y, you have to write out it as 1 times d, y, d, x.
00:21
Just think of it like the chain rule.
00:23
And then the next piece, the derivative of sine is cosine, and it is the chain rule where you leave x, y, alone.
00:30
But then you have to multiply by, well, you have a product rule in here.
00:35
Pr for product rule.
00:37
The derivative of x is one.
00:39
You leave y alone, plus now you leave x alone.
00:42
The derivative of y is d, y, d .y, d .x.
00:48
And then the derivative of one on the right side is equal to zero.
00:52
So if i asked you to solve for d, y, dx, maybe what i would do is distribute that cosine into the problem.
01:00
So we have one plus d .y...