The calculator computes the gradient in 2-dimensions for the variables x and y. It plots the function in 3d and calculates a heatmap with gradient vectors.

Input field for the function:

$f\left(x,y\right)=$

cl
Pos1
End
7
8
9
/
x
y
4
5
6
*
a
b
c
1
2
3
-
(
)
0
.
+
sin
cos
tan
ex
ln
xa
a / x
^
asin
acos
atan
x2
x
ax
|x|
sinh
cosh
c(sin(ax)+ cos(by))
eax sin(by) cos(cx)
ax^2+ by^2+ c
a+√y / b-√x
cy / ax+b
ax+by+c
eax+by
FunctionDescription
sin(x)Sine of x
cos(x)Cosine of x
tan(x)Tangent of x
asin(x)arcsine
acos(x)arccosine of x
atan(x)arctangent of x
atan2(y, x)Returns the arctangent of the quotient of its arguments.
cosh(x)Hyperbolic cosine of x
sinh(x)Hyperbolic sine of x
pow(a, b)Power ab
sqrt(x)Square root of x
exp(x)e-function
log(x), ln(x)Natural logarithm
log(x, b)Logarithm to base b
log2(x), lb(x)Logarithm to base 2
log10(x), ld(x)Logarithm to base 10
more ...

### Function 3d-Plot

x-min=
x-max=
y-min=
y-max=

Parameter values

a=
b=
c=

Parameter ranges

a-min=
b-min=
c-min=
a-max=
b-max=
c-max=

3d-Plot parameter

Color:
Line:
Step x:
Step y:

View

az=
el=
x-Plane y-Plane

Scaling z-Axis

z=
z-min=
z-max=

Heatmap parameter

Grid vectors:
Grid:
Scale:
Opacity:
Saturation:
Brightness:

## Description

A function of the two variables x and y can be defined in the function input field. Up to three parameters a, b and c can be used in the function definition. By selecting the button 'grad(f) ∇f' the gradient of the function is calculated and the function is displayed as a 3d plot. Furthermore, a heatmap is created and the gradient vector field is entered in the headmap.

Both graphics can be extensively parameterized. Changes of the parameters are taken over with the selection 'Update 3d-Plot' or 'Update heatmap'. If the azimuth angle is changed in the 3d plot, the orientation of the heatmap can be adjusted by selecting 'Update heatmap'.

The gradient is the vector build from the partial derivatives of a n-dimensional function f. For the gradient are the two notations are usual. One is grad(f) and the other is with the Nabla operator ∇.

$grad\left(f\right)=\mathrm{\nabla }f=\left(\begin{array}{c}\frac{\mathrm{\partial }f}{\mathrm{\partial }{x}_{1}}\\ \frac{\mathrm{\partial }f}{\mathrm{\partial }{x}_{2}}\\ .\\ .\\ .\end{array}\right)$

### Screenshot of the Image

Print or save the image via right mouse click.

## More Calculators

Here is a list of of further useful calculators:

Index Gradient Derivative calculus Partial derivatives and gradient Derivative fraction Derivative roots Derivative e-function Function Plot ODE first order