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What is a partial derivative?
A partial derivative is the derivative of a function of more than one variable with respect to only one variable. When taking a partial derivative, the other variables are treated as constants. For example, the partial derivative of the function f(x,y)=2x2 + 3xy + y2 with respect to x is:?f/?x = 4x + 3yhere we can see that y terms have been treated as constants when differentiating.The partial derivative of f(x,y) with respect to y is:?f/?y = 3x + 2yand here, x terms have been treated as constants.
Definition of partial differential equation with example?
A partial derivative is the derivative in respect to one dimension. You can use the rules and tricks of normal differentiation with partial derivatives if you hold the other variables as constants, but the actual definition is very similar to the definition of a normal derivative. In respect to x, it looks like: fx(x,y)=[f(x+Δx,y)-f(x,y)]/Δx and in respect to y: fy(x,y)=[f(x,y+Δy)-f(x,y)]/Δy Here's an example. take the function z=3x2+2y we want to find the partial derivative in respect to x, so we can use basic differentiation techniques if we treat y as a constant, so zx'=6x+0 because the derivative of a constant (2y in this case) is always 0. this applies to any number of dimensions. if you were finding the partial in respect to a of f(a,b,c,d,e,f,g), you would just differentiate as normal and hold b through g as constants.
What does partial mean?
Partial in mathematics can refer to:Partial derivatives (derivative of a function with respect to a specific variable, others being held constant)A partial functionPartial can also refer to the regular English usage (referring to an isolated part of the whole).
What is the derivative of x?
The derivative is 2x based on the power rule. Multiply the power by the coefficient of x then drop the power by one.
What is a derivative of atrophy and is atropos a derivative of atrophy?
Atropos is the name of one of the Greek fates, along with Clotho and Lachesis. It is possible that atrophy is derivative of atropos, but not the other way around.
