Introduction:
Gradient: In vector calculus, the gradient is considered as vector field in a function.It points to the points in the route of the maximum rate of increase of the scalar field. Its magnitude is the maximum rate of modify.
Directional derivative: Directional derivative represents the instantaneous rate of modification of the function. It generalizes the view of a partial derivative.
Gradient:
The gradient is defined for the function f(x,y) is as
gradf(x,y)= [gradf(x,y)] = [(delf)/(delx)] i + [(delf)/(dely)] j
This can be calculated by putting the vector operator r to the f(x,y) which is scalar function. That vector field is called as gradient vector field.
Example:
Find the gradient of the function f(x,y)=x+y.
Solution:
Given function is f(x,y)=x+y
[gradf(x,y)] = [(delf)/(delx)i] + [(delf)/(dely)j]
= [(del)/(delx)] (x+y)i+ [(del)/(dely)] (x+y)j
=(1+0)i+(0+1)j
= i+j
Therefore the gradient of the function f(x,y)=x+y is i+j.
Directio...
Derivatives as defined by Warren Buffet are time bombs, both for the companies that make use of them and the monetary framework. Fundamentally these instruments call for cash to change hands at a future date, with the add up to be dictated by one or more reference things, for example, premium rates, stock costs, or money values. Case in point, in the event that you are either long or short a S&P 500 prospects contract, you are a gathering to an extremely straightforward derivatives transaction, with your addition or misfortune determined from developments in the list. Derivatives contracts are of shifting length of time, running now and again to 20 or more years, and their quality is regularly attached to a few Variables.
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