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The equation for the gradient of a linear function mapped in a two dimensional, Cartesian coordinate space is as follows.

The easiest way is to either derive the function you use the gradient formula

(y2 - y1) / (x2 - x1)

were one co-ordinate is (x1, y1) and a second co-ordinate is (x2, y2)

This, however, is almost always referred to as the slope of the function and is a very specific example of a gradient. When one talks about the gradient of a scalar function, they are almost always referring to the vector field that results from taking the spacial partial derivatives of a scalar function, as shown below.

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The equation for the gradient of a function, symbolized ∇f, depends on the coordinate system being used.

For the Cartesian coordinate system:

∇f(x,y,z) = ∂f/∂x i + ∂f/∂y j + ∂f/∂z k where ∂f/(∂x, ∂y, ∂z) is the partial derivative of f with respect to (x, y, z) and i, j, and k are the unit vectors in the x, y, and z directions, respectively.

For the cylindrical coordinate system:

∇f(ρ,θ,z) = ∂f/∂ρ iρ + (1/ρ)∂f/∂θ jθ + ∂f/∂z kz where ∂f/(∂ρ, ∂θ, ∂z) is the partial derivative of f with respect to (ρ, θ, z) and iρ, jθ, and kz are the unit vectors in the ρ, θ, and z directions, respectively.

For the spherical coordinate system:

∇f(r,θ,φ) = ∂f/∂r ir + (1/r)∂f/∂θ jθ + [1/(r sin(θ))]∂f/∂φ kφ where ∂f/(∂r, ∂θ, ∂φ) is the partial derivative of f with respect to (r, θ, φ) and ir, jθ, and kφare the unit vectors in the r, θ, and φ directions, respectively.

Of course, the equation for ∇f can be generalized to any coordinate system in any n-dimensional space, but that is beyond the scope of this answer.

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Q: What is the equation for the gradient of a function?

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The answer will depend on the context. If the curve in question is a differentiable function then the gradient of the tangent is given by the derivative of the function. The gradient of the tangent at a given point can be evaluated by substituting the coordinate of the point and the equation of the tangent, though that point, is then given by the point-slope equation.

y = 4x + 2 It has a slope (gradient) or 4. The slope/gradient of a linear function is simply the number in front of the x when the equation is in the form y=mx+b. (the coefficient of x).

An equation such as y = mx + c is said to be in standard form. From such an equation, Gradient = coefficient of x = 3

Gradient= change in field value divided by the distance

If necessary, rearrange the linear equation so that it is in the slope-intercept form: y = mx + c Then the gradient of the line is m.

10

It's 2. your equation is y=mx+b, so the gradient, or slope, is the "m" in the equation.

If you have the equation, yes. If the equation is given in terms of x and y, make y the subject of the equation. That is, expres the equation in the form y = mx + c where m and c are constants. Then the gradient is m.

15

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>

y = 11x + 5 The slope/gradient of this equation is 11. The slope/gradient can easily been seen in a linear equation: it is simply the co-efficient of x

-5/7

It will just be the gradient of the function, which should be constant in a linear function.

The derivative of a linear function is always its gradientIn the function y = x-1, the gradient is 1 as 1 is the co-efficient of 1x.

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>

The gradient of the function differentiated.

Change the number in front of the X, as that is the gradient.

1

The derivative of a linear function is always its gradientIn the function y = x-1, the gradient is 1 as 1 is the co-efficient of 1x.

You can tell if an equation is a function if for any x value that you put into the function, you get only one y value. The equation you asked about is the equation of a line. It is a function.

maximum value of a function along normal is called gradient. maximum rate of increase of s in magnitude and direction of the point a is called gradient of a scalar

The main function of this structure is to create a concentration gradient in the medulla of the kidney.

Slope or gradient = (y2-y1)/(x2-x1)