Gradient

Gradient Calculator

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

f(...)=

gradf=

=

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

f(...)=

cl
grad(f) ∇f
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

Gradient Notations

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 ∇.

g r a d ( f ) =f= ( f x 1 f x 2 . . . )

Gradient Calculation Rules

For the gradient operation apply the following calculation rules.

g r a d ( c f ) = c g r a d ( f )

g r a d ( f 1 + f 2 ) = g r a d ( f 1 ) + g r a d ( f 2 )

g r a d ( f 1 f 2 ) = f 2 g r a d ( f 1 ) + f 1 g r a d ( f 2 )

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