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人気のある微分積分 >

(\partial)/(\partial y)(x^yln(x))

解

\frac{\partial}{\partial y} (x^{y} ln (x))

解

x^{y} ln^{2} (x)

解答ステップ

\frac{\partial}{\partial y} (x^{y} ln (x))

x

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= ln (x) \frac{\partial}{\partial y} (x^{y})

導関数指数の法則を適用:

\frac{d}{d x} (a^{x}) = a^{x} ln (a)

= ln (x) x^{y} ln (x)

簡素化

ln (x) x^{y} ln (x) : x^{y} ln^{2} (x)

= x^{y} ln^{2} (x)

人気の例

integral from 0 to sqrt(34 of)x^2-17

\int_{0}^{34} x^{2} - 17 d x

(\partial)/(\partial y)(xy+3x-2y)

\frac{\partial}{\partial y} (x y + 3 x - 2 y)

integral from 0 to 1 of x^2+2

\int_{0}^{1} x^{2} + 2 d x

integral of (tan(2/x))/(x^2)

\int \frac{tan ( \frac{2}{x} )}{x ^{2}} d x

sum from n=1 to infinity of (2n+1)/(7^n)

n = 1 \sum \infty \frac{2 n + 1}{7 ^{n}}