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The Sage Tutorial |  |
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The Sage Tutorial | |
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Sage knows how to differentiate and integrate many functions. For example, to differentiate sin(u) with respect to u, do the following:
sage: u = var('u')
sage: diff(sin(u), u)
cos(u)
To compute the fourth derivative of sin(x2):
sage: diff(sin(x^2), x, 4) 16*x^4*sin(x^2) - 12*sin(x^2) - 48*x^2*cos(x^2)
To compute the partial derivatives of x2 + 17y2 with respect to x and y, respectively:
sage: x, y = var('x,y')
sage: f = x^2 + 17*y^2
sage: f.diff(x)
2*x
sage: f.diff(y)
34*y
We move on to integrals, both indefinite and definite. To compute the indefinite integral of x sin(x2) and the definite integral, as x goes from 0 to 1, of x/(x2 + 1):
sage: integral(x*sin(x^2), x) -cos(x^2)/2 sage: integral(x/(x^2+1), x, 0, 1) log(2)/2
To compute the partial fraction decomposition of 1/(x2-1):
sage: f = 1/((1+x)*(x-1))
sage: f.partial_fraction(x)
1/(2*(x - 1)) - 1/(2*(x + 1))
sage: print f.partial_fraction(x)
1 1
--------- - ---------
2 (x - 1) 2 (x + 1)
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The Sage Tutorial | |
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