x^-y - Wolfram|Alpha

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Input

x^(-y)

Contour plot

Contour plot

Partial derivatives

d/dx(x^(-y)) = y (-x^(-y - 1))

d/dy(x^(-y)) = -x^(-y) log(x)

Indefinite integral

integral x^(-y) dx = x^(1 - y)/(1 - y) + constant

Limit

lim_(x->∞) x^(-y) = 0 for y>0

Series representation

x^(-y) = sum_(n=0)^∞ binomial(-y, n) (-1 + x)^n

x^(-y) = sum_(n=0)^∞ (y^n (-log(x))^n)/(n!)

x^(-y) = sum_(n=0)^∞ ((-1 + y)^n (-log(x))^n)/(x n!)

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