Partial Derivatives - Multivariable Calculus

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.
3D Coordinate System: • Plotting Points In a T...
3D Distance Formula: • How To Find The Distan...
Equation of a 3D Sphere: • How To Find The Equati...
Calculus 3 - Intro to Vectors: • Calculus 3 - Intro To ...
Calculus 3 - The Dot Product: • Calculus 3 - The Dot P...
Angle Between Two Vectors: • Finding The Angle Betw...
Parallel & Orthogonal Vectors: • Are The Two Vectors Pa...
Direction Cosines and Vectors: • Calculus 3 - Direction...
Calculus 3 - Vector Projections: • Calculus 3 - Vector Pr...
Cross Product of 2 Vectors: • Cross Product of Two V...
_______________________________________________________________________________________
Area - Vector Cross Product: • Area of a Parallelogra...
Triple Scalar Product: • Volume of a Parallelep...
Vector Equations of Lines: • How To Find The Vector...
The Equation of a Plane: • How To Find The Equati...
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...
_______________________________________________________________________________________
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
Triple Integrals: • Triple Integrals - Cal...
2nd Order - Differential Equations: • Second Order Linear Di...
Undetermined Coefficients: • Method of Undetermined...
Variation of Parameters: • Variation of Parameter...

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It's a great video! I only have one question left... How do I know when the constant becomes 0 or stays the same, when we do differentiate it?

[@realndu]

If we're differentiating with respect to x, y is considered a constant and vice versa. If you're differentiating with respect to one of the variables and the other variable is a stand alone, it will become 0. If the other variable is the product to the variable being differentiated respectively, then its ignored and not made to be 0. Hope this helps :)

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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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