What is the derivative of xe^{-y} ?

The derivative of xe^{-y} is e^{-y}-e^{-y}x(dy)/(dx)

What is the first derivative of xe^{-y} ?

The first derivative of xe^{-y} is e^{-y}-e^{-y}x(dy)/(dx)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

e^{- y} - e^{- y} x \frac{d y}{d x}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

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

= 1 \cdot e^{- y} + (- e^{- y} \frac{d y}{d x}) x

Simplify

= e^{- y} - e^{- y} x \frac{d y}{d x}

\int_{- 2}^{- 1} \frac{2}{x ^{2}} d x

(4 x + 2 x^{- 1} y + 2 x^{- 1} y^{2}) d x + (1 + 2 y) d y = 0

f (x) = \frac{x}{( 1 + x ^{2} )}

2 y d x - x d y = 0

x^{2} - 6 x + 10

What is the derivative of xe^{-y} ?
The derivative of xe^{-y} is e^{-y}-e^{-y}x(dy)/(dx)
What is the first derivative of xe^{-y} ?
The first derivative of xe^{-y} is e^{-y}-e^{-y}x(dy)/(dx)