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The derivative in the direction
of the scalar field is
introduced to characterize the
instantaneous rate of change
of the field function in a given
direction
...

a a  0  a

If

u
 0,
a

then the field function increases in
the direction of this vector
...


The module of the directional
derivative characterizes the
instantaneous rate of change
of the field function in the
direction of a given vector
...


The formula for calculating
the derivative in direction:
u  u
u
u
 cos   cos   cos 
a x
y
z

- partial derivatives;

- direction cosines of the
direction vector
...

Find the derivative of the
function

u  x  y  4yz
2

2

at point М1(0;1;2) from this
point to point М2(2;3;3)
...


The gradient of a scalar field
with a function u(x;y;z)
at some point M(x;y;z)
is a vector, whose coordinates
are the values of the partial
derivatives of the field
function at this point
...

Find the gradient of function

u  x  y  4yz
2

2

at point М1(0;1;2)
...


1
...
To find both quantities, it is
necessary to calculate the
partial derivatives at a given
point of the field function

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