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mahmud_dbm

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In summary, there is confusion over the meaning of ##\frac{d}{dx} y##. It is not clear if it is differentiating a vector ##y## with respect to another vector ##x##, or a vector of functions of the scalar variable ##x## with respect to ##x##. It is also unclear how to define this sort of derivative. Additionally, there is a question of how to differentiate a vector of constants with respect to another vector. However, if there is a function ##f(x)## and a set of constants ##c_1, c_2,...##, it is possible to form the derivatives ##f'(c_1), f'(c_2),...##.

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mahmud_dbm

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Stephen Tashi

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You say that ##x## has exactly N

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mahmud_dbm

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Stephen Tashi said:

You say that ##x## has exactly Nsamples. If ##x## is vector of constants, I don't what you would mean by differentiating with respect to ##x##. If you have some function ##f(x)## and some set of constants ## c_1,c_2,...## you can talk about forming the derivatives ## f'(c_1), f'(c_2),...##.

please let me know if it's okay!

that's how far i have gone, probably it's wrong.

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vela

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mahmud_dbm said:Thank you so much for your reply,

You are right, herexis a vector andHis a matrix, and i want to differentiateHxwith respect to x.

You still haven't explained what ##x## is.

Differentiation over summation is a mathematical operation that involves finding the derivative of a summation. It is commonly used in calculus to find the rate of change of a summation function.

There are several rules for differentiating over summation, including the linearity rule, the power rule, and the chain rule. These rules are similar to the rules for differentiating regular functions, but they are applied to each term in the summation.

No, not all summation functions can be differentiated. Some summation functions are not defined for all values of the variable and therefore cannot be differentiated. Additionally, some summation functions may be too complex to be differentiated analytically.

Differentiating a summation function with multiple variables involves applying the same rules as differentiating a single variable summation function. However, the partial derivatives of each term in the summation should be taken with respect to the corresponding variable.

Yes, differentiation over summation is commonly used in many real-world applications, such as in physics, economics, and engineering. It allows us to calculate rates of change and optimize functions in various fields.

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