- differentiate(expression, var)
but the variable arument may be ommitted if there is only
one variable in the expresstion or if variable x is intended.
For example: differrentiate(sin(x)*exp(x))
partial differentials can also be performed by specifying the intended variable,in the form,
differentiate(2x*y^2 + 3y + z,y)
yield a solution for when the fuction is differentiated with respect to y while other
variables (x and z) are constants.
MathSend can provide solution to both definite and indefinite integrals to
compute an integral. Formats:
- integrate(expression, variable)
- integrate(expression, variable, lower_limit, upper_limit)
For example, integrate(3*y*x^4+8y)
integrate expression with respect to x, while for other variables
the form integrate(3*y/x^4+8yxz, y)
will integrate with
respect to y.
Multiple integrals can also be performed by specifying the order of the variable,
for example integrate integrate(3*y/x^4+8yxz, y, x,x,z
integrates the expression four times: first with
respect to y, second with respect to x, third with respect to x again, and fourth with respect to z.
For definite integrals, the format is : integrate(expression, variable, lower_limit, upper_limit),
for example integrate(3*y/x^4+8yxz, y, 0, inf)
integrate the expression with respect to y from 0 to infinity
Mathsend utilize the Sympy module to compute Limits to a supplied fuction using Gruntz
heuristics and algorithm. Formats:
- limit(expression, variable)
- limit(expression, variable, lower_limit, upper_limit)
The format is limit(expression, variable, lower_limit, upper_limit).
For example: limit(x*sin(1/x), x, inf)
Asymptotic series expansions can be computed with the series keywords.
- series(expression, variable)
- series(expression, variable, x0, upper_limit)
if the x0
ans order values are not specified (that is, any of the first two formats)
x0 will be taken as 0 while the order as 6. For example:
series(sin(x)) computes the Taylor series of sin(x) up to the order of series; and for a higher order of
the series, say 9, use series(sin(x),0,9).
For a different initial value, say 2, with the solution required up to the 9th order of x, we have series(sin(x), x, 2, 9)