Formal definition of partial derivatives

Partial derivatives are formally defined using a limit, much like ordinary derivatives.

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[papername]

That h notation is really just there to cause confusion. Thank you for pointing out what it really just it.

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[Adam]

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[curtpiazza]

Thank you for clarifying ...great explanation! 🎉

[JrDarkPhantom]

When he wrote the limits, he didn't extend the fraction signs for the entire numerator... It should include all of [F(a+h, b) - F(a, b)]. I hope no one was confused by that.

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Whenever I hear that voice, I know I'm going to learn some _real math!
WE LOVE YOU GRANT SANDERSON!!!

[JoaoJGabriel]

at 0:55 f(x) gets prettier as the value of x increases

[wast]

Really interseting approach of interpreting the derivative 5:13

[BigNWide]

Why is h used for a nudge in the x direction? I suspect it is related to the use of (h, k) to represent the image of the origin for a geometric transformation. The variable h is used there as well for a shift in the x direction.

[tdavis]

you could start this from about 7 minutes and go from there, refer to prev lessons will save time. also, could mention that the new thing is each value (x, y, z, i, , j, k...) just becomes a function, after that its all familiar but now for n dimensional geometries

[ndianzon]

(a, f(a)) and (b, f(b)) are points on the graph x^2 and h = b - a, solve for b, b = h+a, then (a, f(a)) and (h+a, f(a+h)). slope = f(a+h) - f(a)/h

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how can i find out which playlist is this video from ?

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"room for rigour"
Funny phrase right

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[mstevens]

Shouldn't the partial derivative be "del" not "d"?

[thomasdiprima]

Sorry, but Grant takes 10 minutes to explain something that Sal can do in five minutes. When you go into that much detail it tends to get muddled.