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Gradient= change in field value divided by the distance
Assume you want to know what is the formula of the gradient of the function in multivariable calculus. Let F be a scalar field function in n-dimension. Then, the gradient of a function is: ∇F = <fx1 , fx2, ... , fxn> In the 3-dimensional Cartesian space: ∇F = <fx, fy, fz>
Assume you want to know what is the formula of the gradient of the function in multivariable calculus. Let F be a scalar field function in n-dimension. Then, the gradient of a function is: ∇F = <fx1 , fx2, ... , fxn> In the 3-dimensional Cartesian space: ∇F = <fx, fy, fz>
If you think of it as a hill, then the gradient points toward the top of the hill. With the same analogy, directional derivatives would tell the slope of the ground in a direction.
It is the rate of change in the vector for a unit change in the direction under consideration. It may be calculated as the derivative of the vector in the relevant direction.