To calculate result you have to disable your ad blocker first.
ADVERTISEMENT
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) --
ADVERTISEMENT