en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (x^2+1e^{-x})

Solution

\frac{d}{d x} ((x^{2} + 1) e^{- x})

Solution

2 e^{- x} x - e^{- x} (x^{2} + 1)

Solution steps

\frac{d}{d x} ((x^{2} + 1) e^{- x})

Apply the Product Rule:

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

f = x^{2} + 1, g = e^{- x}

= \frac{d}{d x} (x^{2} + 1) e^{- x} + \frac{d}{d x} (e^{- x}) (x^{2} + 1)

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

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

= 2 x e^{- x} + (- e^{- x}) (x^{2} + 1)

Simplify

= 2 e^{- x} x - e^{- x} (x^{2} + 1)

Popular Examples

derivative of y=(7x-3)/(5x+4)+x^3 derivative of

y = \frac{7 x - 3}{5 x + 4} + x^{3}

integral of 8e^{2x}

\int 8 e^{2 x} d x

derivative of (x^2+5^3)

\frac{d}{d x} ((x^{2} + 5)^{3})

d/(dt)(3e^{2t})

\frac{d}{d t} (3 e^{2 t})

integral of cos^2(2aθ)

\int cos^{2} (2 a θ) d θ

Frequently Asked Questions (FAQ)

What is the derivative of (x^2+1e^{-x}) ?
The derivative of (x^2+1e^{-x}) is 2e^{-x}x-e^{-x}(x^2+1)
What is the first derivative of (x^2+1e^{-x}) ?
The first derivative of (x^2+1e^{-x}) is 2e^{-x}x-e^{-x}(x^2+1)