The calculator computes the gradient for the given variables (co-ordinates) defined in the input field.

$f\left(\mathrm{...}\right)=$

$gradf=$

=

Input fields for the function and the co-ordinates for the gradient calculation:

$f\left(\mathrm{...}\right)=$

 clear grad(f) , ∇f Pos1 Ende 7 8 9 / $x$ $y$ $z$ 4 5 6 * ( ) 1 2 3 - a b c 0 . + $\mathrm{sin}$ $\mathrm{cos}$ $\mathrm{tan}$ ${e}^{x}$ $\mathrm{ln}\left(x\right)$ ${x}^{a}$ ^ $\mathrm{asin}$ $\mathrm{acos}$ $\mathrm{atan}$ ${x}^{2}$ $\sqrt{x}$ $\sqrt[3]{x}$ $\sqrt[4]{x}$ $\frac{\left(\right)}{\left(\right)}$ $\mathrm{sinh}$ $\mathrm{cosh}$ $\frac{ax+c}{by+c}$ $\frac{a+z}{b+x}$ $\frac{{y}^{2}-{a}^{2}}{{z}^{2}+{a}^{2}}$ $\frac{1}{a+bx}$ $\frac{1+\sqrt{x}}{1-\sqrt{y}}$ $\sqrt{x+a}$ $\sqrt{{e}^{ax}}$ ${e}^{\sqrt{z}}$ $a{e}^{-b{x}^{2}+c}$ $\frac{\mathrm{sin}\left(x\right)}{\mathrm{cos}\left(x\right)}$ $a{x}^{2}+bz+c$ ${e}^{x}\cdot \mathrm{sin}\left(y\right)\cdot \mathrm{cos}\left(z\right)$ $\frac{1}{\sqrt{ax}}$ $a{e}^{bx+c}$ ${e}^{ax}$ ${e}^{a{x}^{2}}$ $\frac{1}{{e}^{ax}}$ $\frac{x}{{e}^{x}}$ $\frac{1}{\mathrm{sin}}$ $\frac{1}{\mathrm{cos}}$ $\frac{1}{\mathrm{tan}}$ $a\cdot \mathrm{sin}\left(bx+c\right)$ $a\cdot \mathrm{cos}\left(bx+c\right)$ $a\cdot \mathrm{tan}\left(bx+c\right)$ $a\cdot {\mathrm{sin}}^{2}\left(bx+c\right)$

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 ∇.

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

## Gradient Calculation Rules

For the gradient operation apply the following calculation rules.

$grad\left(c\cdot f\right)=c\cdot grad\left(f\right)$

$grad\left({f}_{1}+{f}_{2}\right)=grad\left({f}_{1}\right)+grad\left({f}_{2}\right)$

$grad\left({f}_{1}\cdot {f}_{2}\right)={f}_{2}\cdot grad\left({f}_{1}\right)+{f}_{1}\cdot grad\left({f}_{2}\right)$

## More Calculators

Here is a list of of further useful calculators:

Index Derivative calculus Partial derivatives and gradient Derivative fraction Derivative roots Derivative e-function Derivative sine cosine tangent Derivative sinh cosh tanh Derivative table Gradient 2d Plot Function Plot ODE first order