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:

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

Co-ordinates:
cl
Pos1
End
7
8
9
/
Δ
x
y
z
4
5
6
*
Ω
a
b
c
1
2
3
-
μ
π
(
)
0
.
,
+
ω
sin
cos
tan
ex
ln
xa
a / x
^
σ
asin
acos
atan
x2
x
ax
a / x+b
|x|
δ
sinh
cosh
a⋅x+c / b⋅y+c
a+x / b+z
z2-a2/ z2+a2
a / x+b
1+√y / 1-√y
exsin(y)cos(z)
x+a
ea⋅x
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 ...

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 ∇.

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

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