00:01
Say we have this function, 3x cube times y equals 6, and we want to find its derivative at a point, specifically at the point 1, 2.
00:11
Well, first of all, we must notice that this equation is written implicitly, meaning that the x and the y are in the same side of the equation.
00:19
They're kind of mixed together.
00:21
Another way we can say that is that the y is not alone.
00:24
Although we could easily solve for y in this case, we could also use implicit differentiation, which is what we're going to practice now.
00:31
So i like to use this notation when i'm taking a derivative.
00:34
Applying the product rule, considering this our first function and this our second function, the two functions that are being multiplied.
00:42
Taking the derivative of the first function, we have 3 times 3x squared.
00:47
Notice that's power rule times the second function stays the same, plus keeping the first function the same.
00:55
So 3x cubed times find the derivative of the second function, which would be one.
01:00
The derivative of y is 1.
01:03
However, since it is a y, we will write d, y, d, x.
01:07
So that's 1 times d, y, d, x, not writing the 1...