14.3: Partial Derivatives

[@elijahnicpon]

Georgia Tech student here. Your students are so so so so so lucky to have you. You explain things 10x better, are 10x nicer, and are 10x more clear than my mean tenured professor. I think ~1/2 of my 300 person lecture uses your videos over my professor's lectures. Thank you for single handedly carrying the curve of Z. Lin's Fall 2022 Math 2550 Section G.

[@shawhg470]

felt that

[@SWE-from-Sweden]

And we're still using them a year later - thank you for your help!

[@rameezmalik8263]

Thank you for this!!!

[@kanishkachaudhary4749]

In example 4 fyy is 6x+ 10x^2.. You made silly error

[@azizkash286]

bless your soul

[@prashanthalai1413]

Ma'am i still didn't get it why is our goal to find partial of z with respect to y can you please explain. And how can we determine that our z is the dependent variable.

[@forodtu]

in the las texercise, how did we write dz/dy=-y/z

[@alexandraniedden5337]

I moved 2y to the other side, giving 2z(dz/dy) = -2y. Dividing by 2z gives dz/dy = -y/z.

[@kasper-nawaf8169]

THE BEST !

[@zuhairshah]

for the last example, could you have found the derivative of dx/dy and the answer would still be correct?

[@ayytea9431]

I tried it out and in this example, yes because x and z coordinate are the same.

[@SubikaHaider]

in the last exercise, why did we set our gosl as dz/dy and not dx/dy?

[@alexandraniedden5337]

Our dependent variable here is z, whereas x and y are independent. The slope in the y direction will be the rate at which z is changing as y changes.

[@jeremygrafals7077]

dz/dy = -y/z I don't understand how she got there.

[@s7vxn]

2y+(2z•[dz/dy]) = 0 • Subtract 2y from both sides 2z•[dz/dy] = -2y • Divide by 2z on both sides dz/dy = -2y/2z • Simplify dz/dy = -y/z

[@7mood593]

in 21:40 isn't fxx = 10y?

[@greensparkles6796]

No, y is a constant so y^2 is left alone and you only take the derivative of (x) = 1. 10(1)y^2 = 10y^2