00:01
We are given a function 2x squared plus 3xy minus 3y cubed equals 176.
00:08
We wish to find the tangent slope at the point of 4, negative 4.
00:13
We're going to use what's called implicit differentiation since our original equation contains both x and y's intermingled.
00:22
The derivative of 2x squared with respect to x is 4x.
00:29
3xy has two variables.
00:31
We're going to consider this to be a product.
00:36
We'll say the first term is 3x and the second term is y.
00:40
Product rule derivative tells us that we have first times the derivative of the second.
00:47
The second is y and its derivative is unknown, so we'll call that y prime.
00:53
So that's first derivative of the second plus second y times the derivative of the first and the derivative of 3x is 3, which i'll just put in front.
01:05
For the 3y cubed, well i do have a minus, that's going to be treated like a chain because i don't know what the derivative of y is.
01:20
So i bring the power out front, 3 times 3 will give us 9, subtract one from the old and then multiply by the derivative of the inside, which is the unknown y prime.
01:33
On the right side, the derivative of 176 is 0.
01:38
We do need to isolate the y prime...