D¶

Symbolic differentiation. D[expr, x] differentiates once, D[expr, {x, n}] differentiates n times, D[expr, x, y] takes mixed partial derivatives.

$ wo 'D[Sin[x], x]'
Cos[x]

$ wo 'D[x^2 + 3 x + 5, x]'
3 + 2*x

$ wo 'D[x^2 y, {x, 2}]'
2*y

Squaring a derivative distributes the sign correctly, so the Pythagorean speed of a unit circle collapses cleanly:

$ wo 'D[Cos[t], t]^2'
Sin[t]^2

$ wo 'D[Cos[x], x]^2 + D[Sin[x], x]^2'
Cos[x]^2 + Sin[x]^2

Differentiating a power series with respect to its expansion variable applies the term-by-term power rule:

$ wo 'D[Series[Exp[x], {x, 0, 4}], x]'
SeriesData[x, 0, {1, 1, 1/2, 1/6}, 0, 4, 1]

$ wo 'D[SeriesData[x, 0, {1, 1, 1}, 0, 3, 1], x]'
SeriesData[x, 0, {1, 2}, 0, 2, 1]