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Say you have a function of a single variable, f(x). Then there is no ambiguity about what you are taking the derivative with respect to (it is always with respect to x).
But what if I have a function of a few variables, f(x,y,z)? Now, I can take the derivative with respect to x, y, or z. These are "partial" derivatives, because we are only interested in how the function varies w.r.t. a single variable, assuming that the other variables are independent and "frozen".
e.g., Question: how does f vary with respect to y? Answer: (partial f/partial y)
Now, what if our function again depends on a few variables, but these variables themselves depend on time: x(t), y(t), z(t) --> f(x(t),y(t),z(t))? Again, we might ask how f varies w.r.t. one of the variables x,y,z, in which case we would use partial derivatives. If we ask how f varies with respect to t, we would do the following:
df/dt = (partial f/partial x)*dx/dt + (partial f/partial y)*dy/dt + (partial f/partial z)*dz/dt
df/dt is known as the "total" derivative, which essentially uses the chain rule to drop the assumption that the other variables are "frozen" while taking the derivative.
This framework is especially useful in physical problems where I might want to consider spatial variations of a function (partial derivatives), as well as the total variation in time (total derivative).
What else can I help you with?
A polar molecule has a partial positive side and a partial negative side?
Yes, that's correct. A polar molecule has an uneven distribution of electrons, leading to regions of partial positive and partial negative charge. This occurs when there is a difference in electronegativity between the atoms within the molecule.
What is the bond polarity of CO?
The bond between carbon and oxygen in CO is polar due to the difference in electronegativity between the two atoms. Oxygen is more electronegative than carbon, leading to a partial negative charge on the oxygen atom and a partial positive charge on the carbon atom.
If the electronegativity difference between elements X and Y is 2.1 the bond between the elements X-Y is?
The bond between elements X and Y would be considered as polar covalent since the electronegativity difference is 2.1. In a polar covalent bond, the shared electrons are drawn more towards the more electronegative element, resulting in a partial positive charge on the less electronegative element and a partial negative charge on the more electronegative element.
Which gas law explains why there is as much CO2 exchanged between the alveoli and blood as there is O2 exchanged despite the fact that the partial pressure difference is so much smaller for CO2?
Henry's Law explains that the amount of gas dissolved in a liquid is directly proportional to the partial pressure of that gas above the liquid. As CO2 is more soluble in blood than O2, even though the partial pressure difference is smaller for CO2, more CO2 can be exchanged between the alveoli and blood due to its higher solubility.
Is HP polar or nonpolar?
HP (phosphorus hydride) is a polar molecule due to the difference in electronegativity between phosphorus and hydrogen atoms, causing an uneven distribution of electron density. This results in a partial positive charge on the hydrogen atom and a partial negative charge on the phosphorus atom.
What is the difference between total differentiation and partial differentiation?
Suppose, Z is a function of X and Y. In case of Partial Differentiation of Z with respect to X, all other variables, except X are treated as constants. But, total derivative pf z is given by, dz=(partial derivative of z w.r.t x)dx + (partial derivative of z w.r.t y)dy
Why do you need total derivative and partial derivative?
The partial derivative only acts on one the variables on the equations and treats the others as constant.
The difference between differential and derivative?
They are the same thing.
What is the difference between a definition and derivative?
a definition is what it means, a derivative is what it derives from, like a root word
What is the difference between anti-derivative and integral?
there is no diffference, i think...
What is the derivative of binary cross entropy and how is it calculated?
The derivative of binary cross entropy is calculated by taking the difference between the predicted probability and the actual label. This difference is then multiplied by the input data to get the derivative.
What are spacial derivatives?
The spacial derivative is the measure of a quantity as and how it is being changed in space. This is different from a temporal derivative and partial derivative.
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.
What are the applications of partial derivatives in real analysis?
what are the applications of partial derivative in real analysis.
What is the derivative of a function with respect to a vector?
The derivative of a function with respect to a vector is a matrix of partial derivatives.
What is the partial derivative of the van der Waals equation with respect to volume?
The partial derivative of the van der Waals equation with respect to volume is the derivative of the equation with respect to volume while keeping other variables constant.
What is difference between anti integration and derivative?
In all but very exceptional cases there is no difference.
