D
D[
f
,
x
]
gives the partial derivative
.
D[
f
,
{
x
,
n
}]
gives the multiple derivative
.
D[
f
,
,
,
...
]
gives
.
can be used to find the rate of change of a function.
D[
f
,
x
]
can be input as
. The character
is entered as
pd
or
\
[PartialD]
. The variable
x
is entered as a subscript.
An alternative notation for taking the derivative of a function of one variable is
f
'
[
x
]
which is equivalent to
D[
f
[
x
]
,
x
]
.
▢
f
''
[
x
]
denotes the second derivative of
f
x
All quantities that do not explicitly depend on the
are taken to have zero partial derivative.
The derivatives of built-in mathematical functions are evaluated when possible in terms of other built-in mathematical functions.
D
uses the chain rule to simplify derivatives of unknown functions.
D[
f
,
x
,
y
]
can be input as
. The character
\
[InvisibleComma]
, entered as
,
, can be used instead of an ordinary comma. It does not display but is still interpreted just like a comma.
See also:
Integrate
,
ND
.
Examples
Using InstantCalculators
Here are the InstantCalculators for the
D
function. Enter the parameters for your calculation and click
Calculate
to see the result.
In[1]:=
Out[1]=
In[2]:=
Out[2]=
Entering Commands Directly
You can paste a template for this command via the Text Input button on the
D
Function Controller.
Here is the derivative of
with respect to
x
.
In[3]:=
Out[3]=
In[4]:=
Out[4]=
Here is the Chain Rule of first-year calculus.
In[5]:=
Out[5]=
If you differentiate a function with respect to
x
, say, all other parameters are treated as constants.
In[6]:=
Out[6]=
This gives the fourth derivative of
with respect to
x
.
In[7]:=
Out[7]=
Here is the partial derivative
.
In[8]:=
Out[8]=
Mathematical Input Notation
This
also gives
the fourth derivative of
with respect to
x
.
In[8]:=
Out[8]=
This
also gives
the partial derivative
.
In[9]:=
Out[9]=
