Calculus 3: Partial Derivative (5 of 30) Find the Partial Derivative: Example 1

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In this video I will find the partial derivative with-respect-to x and y of f(x,y)=y^4+5xy and f(x,y)=5(x^4)(y^3-2(x^3)y.

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This is just amazing, most of us know how to differentiate functions but the conventional school method doesnt teach us why we do it and what is the logic behind it. But your videos, Sir, it is a treasure.. thank you so much sir.

yogahariharan
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Thank you for this excellent explanation.

valeriereid
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Why does yˆ4 disappear in the first partial with regard to x but yˆ3 survives in the second example? Seems like yˆ4 should be in first example as constant.

Walter-uyor
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How come the derivative of y^4 in the first one is equal to zero because it’s a constant but yet all of the other constants in the rest remains the same?

MegaJayLover
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Thank you, I think I am kind of getting it now... So if we differentiate with respect to x and something is multiplied by y we just write y without applying changes to it. If we have +/- 3y following that for example, then we drop "3y" completely? I have a poor level of understanding how derivation works...

annakopyl
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Hi Michel, is this course complete? Cause in my university, we learn about Topology (open and closed balls and sets), Analytic Geometry (quadratics and conics), vector and scalar functions...

notSavant
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Shouldn't the final function of y read: 5x^43y^2-2x^3?

tomjenkins