ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

d/(dy)(y^2e^{xy})

解

\frac{d}{d y} (y^{2} e^{x y})

解

2 y e^{x y} + e^{x y} x y^{2}

解答ステップ

\frac{d}{d y} (y^{2} e^{x y})

x

を定数として扱う

積の法則を適用:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = y^{2}, g = e^{x y}

= \frac{d}{d y} (y^{2}) e^{x y} + \frac{d}{d y} (e^{x y}) y^{2}

\frac{d}{d y} (y^{2}) = 2 y

\frac{d}{d y} (e^{x y}) = e^{x y} x

= 2 y e^{x y} + e^{x y} x y^{2}

人気の例

derivative of xcsc(x-cot(x))

\frac{d}{d x} (x csc (x) - cot (x))

sum from n=0 to infinity of 6/(2^n)

n = 0 \sum \infty \frac{6}{2 ^{n}}

derivative f(x)=(-6)/x

d er i v a t i v e f (x) = \frac{- 6}{x}

(\partial)/(\partial x)(-8xy-2x^4-2y^4)

\frac{\partial}{\partial x} (- 8 x y - 2 x^{4} - 2 y^{4})

limit as x approaches 0 of (6^x-5^x)/x

x \to 0 lim (\frac{6 ^{x} - 5 ^{x}}{x})