00:01
Here, we're given an equation and we're asked to use implicit differentiation to find the slope of the tangent line to the curve at a given point.
00:08
So what we need to do is start off by just taking the derivative.
00:11
When we do implicit differentiation, it's the same as the regular differentiation.
00:16
Just remember that derivative of y is not one.
00:19
It's y prime.
00:20
So to start off with, i have the quotient rule, which says i take the derivative of the first, or the top, which is y prime, and i multiply by the bottom x minus 9y on change.
00:31
And then i subtract the derivative of the bottom, which is 1 minus 9y prime, since the derivative of y is y prime, times the top unchanged.
00:42
And then i divide by x minus 9y squared.
00:47
Equals, now i take the derivative of the second side.
00:49
So that's 4x cubed.
00:51
And that's it because the 8 goes away as a constant...