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Explain whether atomic number can increase during nuclear decay .Support your answer with example.

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Ans.When a beta particle is emitted out of any nucleus,then it's mass number does not undergo any change but it's charge number increase by one.Negative Beta is an electron and its emission from the nucleus becomes an in comprehensive enigma, as there is no electron in the nucleus >how ever , the emission of electrom from the nucleus can be thought of as neutron emitting an electron and becoming a proton, although the modern explanation is not that simple.
This means that beta particle is formed at the time of emission.That is why at the time of emission of a beta particle the charge number of nucleus increases by one.

For Example:

what is a directional derivative/gradient?

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Directional Derivative The directional derivative  is the rate at which the function  changes at a point in the direction . It is a vector form of the usual derivative, and can be defined as (1) (2) where  is called "nabla" or "del" and  denotes a unit vector. The directional derivative is also often written in the notation (3) (4) where  denotes a unit vector in any given direction and  denotes a partial derivative. Let  be a unit vector in Cartesian coordinates, so (5)