Partial Derivatives - Multivariable Calculus
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- เผยแพร่เมื่อ 28 ก.ย. 2024
- This calculus 3 video tutorial explains how to find first order partial derivatives of functions with two and three variables. It provides examples of differentiating functions with respect to x or with respect to y using techniques such as the product rule, quotient rule, and power rule. This video contains plenty of examples and practice problems.
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Planar Equation - 3 Points: • How To Find The Equati...
Lines & Planes - Intersection: • How To Find The Point ...
Angle Between Two Planes: • How To Find The Angle ...
Distance Between Point and Plane: • How To Find The Distan...
Chain Rule - Partial Derivatives: • Chain Rule With Partia...
Implicit Partial Differentiation: • Implicit Differentiati...
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Directional Derivatives: • How To Find The Direct...
Limits of Multivariable Functions: • Limits of Multivariabl...
Double Integrals: • Double Integrals
Local Extrema & Critical Points: • Local Extrema, Critica...
Absolute Extrema - Max & Min: • Absolute Maximum and M...
Lagrange Multipliers: • Lagrange Multipliers
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Okay it took me a good little while to figure this out, but apparently when it comes to 'constants', we don't take the derivative and instead just rewrite it unchanged whenever it is attached (multiplied) to the other variable that we are differentiating in respect to.
If it is just by itself, THEN we take the derivative of it, which is zero.
I had been so confused why he would say 'this is a constant' and would sometimes just rewrite it unchanged, while other times write it as zero. I'm glad that I figure it out. 😆
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Finding higher ordered partial derivatives at 44:43. That's fxx , fxy, fyy, fyx
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At 23:29, the derivative of 4xy² should be 8y since x is a costant...
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In the problem In(x^2/y),I think is better if you re-write the lin, in the form of (Inx^2-Iny).Just an opinion.
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@ 16:59 what happens to the power of -1/2 , why does it not go to the denominator as positive?
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Yea at 28:29 u can still do qoutient rule but treat y as contant, im a potato btw. Love your vids 💙
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Thank you for the great videos, when do we know that the other variable that we are not differentiating with respect to, must remain as it is or it must be zero?
When there is an addition or substraction operation that's when the variable not being derived is 0
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I am confused on the first question of the video, for fy why does 7x^2 go to 0 but 5x^4 does not? Why do we treat some x as a constant and some not. Should'nt all the x's go to zero? same for the fx shouldnt all y's go to zero as well since they are all technically constants?
Edit: Is it because the 7x^2 is alone and not multiplied by y?
Yes
Yeahh
If I recall correctly the derivative of a constant*variable= the constant*(derivative of the variable)
For example
d/dx(2x)=2, and not zero even though 2 is a constant and would be zero if by itself
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