Gradient

Gradient Calculator

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

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

f...=

clear

grad(f) , ∇f

Pos1

Ende

7

8

9

/

x

y

z

4

5

6

*

(

)

1

2

3

-

a

b

c

0

.

+

sin

cos

tan

ex

ln(x)

xa

^

asin

acos

atan

x2

x

x3

x4

()()

sinh

cosh

ax+cby+c

a+zb+x

y2-a2z2+a2

1a+bx

1+x1-y

x+a

eax

ez

ae-bx2+c

sinxcosx

ax2+bz+c

exsinycosz

1ax

aebx+c

eax

eax2

1eax

xex

1sin

1cos

1tan

asinbx+c

acosbx+c

atanbx+c

asin2bx+c

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 Gradient 2d Plot Function Plot ODE first order