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:
$f\left(x,y\right)=$
Function | Description |
---|---|
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 a^{b} |
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 |
Parameter values
Parameter ranges
3d-Plot parameter
View
Scaling z-Axis
Heatmap parameter
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 ∇.
$grad(f)=\mathrm{\nabla}f=\left(\begin{array}{c}\frac{\mathrm{\partial}f}{\mathrm{\partial}{x}_{1}}\\ \frac{\mathrm{\partial}f}{\mathrm{\partial}{x}_{2}}\\ .\\ .\\ .\end{array}\right)$
Print or save the image via right mouse click.
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