##### x^3+6xy+y^2= 8

Raw Transcript

Hello again everybody. Tom from everystepcalculus.com and everystepphysics.com.

Calculus problem regarding a tangent line with a curve. Dealing with two variables. I show you how that works on my programs. Index 8 to get to my menu. I’m already at equation of a tangent line here to save time. And you’ll scroll down to it and then you’ll enter the function Alpha, you have to press alpha before you enter anything into these entry lines. Alpha x cubed plus 6 times x times y plus y squared minus 8 equals zero. You always have to transpose everything on the other side of the equation here and bring it over the left side and make zero on the right or a number on the right either one would work. Now because you’ve entered y in here this is going to be an implicit differentiation problem. So here’s the formula here that you just entered. In the implicit system. And it looks pretty good. I say it’s ok. Differentiate both sides of the equation with respect to x. So here we go both sides. We’re going to do each one individually. This one here because xy, we need the product rule. So you can write the product rule down and do it like this or you can just keep clicking and you’ll finally get to the product rule answer to which is this right here and 6x dy dx and we keep going. y squared is equal to this because it’s a y dy dx also. And you combine the functions, dy dx here and then no dy dx just regular X Y and the implicit answer is this right here minus 3x squared minus 6x, etc. Division sign here, you know. Now we’re going to evaluate it at a point and the point is alpha 1 and alpha 1. So xy is 11. I say it’s okay. We enter those variables into the numerator and the denominator, come up with a slope of minus 98. Slope of the line and then we figure that y equals mx plus b which is here is the slope, m, and then you add the 1 for the x and 1 for the y and then figure out what b is here. Subtract this from 1, 1 of course 8 eighths and you subtract you get 17 eighths. Subtracting a minus so you get 17 eighths. Here’s the answer y equals mx plus b. Pretty neat, huh? everystepcalclus.com you can go, and I also give you that angle of the line is pointing, notice that it’s pointing in this direction not up but down to the right and if you want to do it and other points, it’ll take you back there. Pretty neat, huh? everystepcalclus.com Go to my site, buy my programs if you want to pass calculus and subscribe if you want to see more videos that I might make you. Have a good one!

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