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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

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

Simplify

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

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