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Gradient Calculator
Enter the vector function and the values of the point in the gradient calculator. Click calculate to solve.
Table of Contents:
Gradient Calculator
This gradient calculator finds the partial derivatives of functions. You can enter the values of a vector line passing from 2 points and 3 points. For detailed calculation, click “show steps”.
What is a Gradient?
The gradient is similar to the slope. It is represented by ∇(nabla symbol). A gradient in calculus and algebra can be defined as:
“A differential operator applied to a vector-valued function to yield a vector whose components are the partial derivatives of the function with respect to its variables.”
Gradient Formula
-- \nabla f (x, y, z) = \Huge [ \small \begin{array}{ccc} \dfrac{df}{dx}\\ \\ \dfrac{df}{dy}\\ \\ \dfrac{df}{dz} \end{array} \Huge]A gradient is calculated by finding the partial derivative of the function with respect to the variable.
How to calculate gradient?
Example:
A function is x2 + y2. Find its gradient for point (2,2).
Solution:
Step 1: Find the differentiate.
-- \nabla f = \Big( \dfrac{df}{dx}, \dfrac{df}{dy} \Big)=ddx[d(x2+ y2) , = ddy[d(x2+ y2) --
-- =\dfrac{d}{dx}[d(x^2+ y^2) \enspace ,=\dfrac{d}{dy}[d(x^2+ y^2) --
-- =d(\dfrac{d}{dx}[x^2]+\dfrac{d}{dx}[y^2]) \enspace, = d(\dfrac{d}{dy}[x^2]+\dfrac{d}{dy}[y^2]) --
-- = d (2x + 0) \enspace , = d (0 + 2y) --
-- = 2x , = 2y --
Step 2: Plug in the point.
-- \nabla f (x,y) = [(2)(x) , (2)(y)] --
-- \nabla f (2,2) = [(2)(2) , (2)(2)] --
= 4 , 4
Step 3: Write equation.
-- \nabla(x^2+y^2)(x,y)=(2x , 2y) --
-- \nabla(x^{2} + y^{3})|_{(x,y)=(2,2)} = (4,4) --
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