Dt
Details and Options
- Dt[f,x1,…,Constants->{c1,…}] specifies that the ci are constants, which have zero total derivative.
- Symbols with attribute Constant are taken to be constants, with zero total derivative.
- If an object is specified to be a constant, then all functions with that object as a head are also taken to be constants.
- All quantities not explicitly specified as constants are assumed to depend on the xi.
- You can specify total derivatives by assigning values to Dt[f], etc.
Examples
open all close allBasic Examples (4)
Find the total derivative with respect to 
:
Dt[a x + b, x]Find the total differential of 
:
Dt[x y]Find the second total derivative with respect to 
:
Dt[x ^ 2 y, {x, 2}]Find the total derivative with respect to two variables:
Dt[x ^ 2 y, x, y]Scope (4)
The total derivative of a constant is 0:
Dt[1]Attributes[E]Dt[E]Total derivative of a general monomial:
Dt[a x ^ n, x]Total derivative of a trigonometric function:
Dt[Sin[x y], x]Rules for total differentiation including sums:
Dt[f + g]Dt[f g]Together[Dt[f / g]]Dt[f[g]]Dt[Log[f]]Options (3)
Constants (3)
Specify that 
is constant with respect to 
:
Dt[a x ^ 2 + b, x, Constants -> {a}]Specify that 
and 
are constant with respect to 
:
Dt[a x ^ 2 + b, x, Constants -> {a, b}]Use TagSet to specify a constant:
y/:Dt[y, x] = 0D[2 x y, x]
Text
Wolfram Research (1988), Dt, Wolfram Language function, https://reference.wolfram.com/language/ref/Dt.html.
CMS
Wolfram Language. 1988. "Dt." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Dt.html.
APA
Wolfram Language. (1988). Dt. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Dt.html