What is (\partial)/(\partial x)((xy-2)e^{-xy}) ?

The answer to (\partial)/(\partial x)((xy-2)e^{-xy}) is -e^{-xy}xy^2+3e^{-xy}y

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)((xy-2)e^{-xy})

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

- e^{- x y} x y^{2} + 3 e^{- x y} y

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

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

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

\frac{\partial}{\partial x} (x y - 2) = y

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

= y e^{- x y} + (- y e^{- y x}) (x y - 2)

Simplify

y e^{- x y} + (- y e^{- y x}) (x y - 2) : - e^{- x y} x y^{2} + 3 e^{- x y} y

= - e^{- x y} x y^{2} + 3 e^{- x y} y

\frac{( ( 2 x + 5 ) ^{7} )}{14}

x^{4} - 8 x^{2} + 16

\frac{d}{d x} (\frac{- 3}{x - 6} - 2)

\frac{d}{d x} (0.8 \cdot x^{4})

\int x sin^{2} (x) cos^{3} (x) d x

What is (\partial)/(\partial x)((xy-2)e^{-xy}) ?
The answer to (\partial)/(\partial x)((xy-2)e^{-xy}) is -e^{-xy}xy^2+3e^{-xy}y