What is the derivative of y=2xe^{-3x}+3e^{x^2} ?

The derivative of y=2xe^{-3x}+3e^{x^2} is 2(e^{-3x}-3e^{-3x}x)+6e^{x^2}x

What is the first derivative of y=2xe^{-3x}+3e^{x^2} ?

The first derivative of y=2xe^{-3x}+3e^{x^2} is 2(e^{-3x}-3e^{-3x}x)+6e^{x^2}x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

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

2 (e^{- 3 x} - 3 e^{- 3 x} x) + 6 e^{x^{2}} x

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (2 x e^{- 3 x}) + \frac{d}{d x} (3 e^{x^{2}})

\frac{d}{d x} (2 x e^{- 3 x}) = 2 (e^{- 3 x} - 3 e^{- 3 x} x)

\frac{d}{d x} (3 e^{x^{2}}) = 6 e^{x^{2}} x

= 2 (e^{- 3 x} - 3 e^{- 3 x} x) + 6 e^{x^{2}} x

What is the derivative of y=2xe^{-3x}+3e^{x^2} ?
The derivative of y=2xe^{-3x}+3e^{x^2} is 2(e^{-3x}-3e^{-3x}x)+6e^{x^2}x
What is the first derivative of y=2xe^{-3x}+3e^{x^2} ?
The first derivative of y=2xe^{-3x}+3e^{x^2} is 2(e^{-3x}-3e^{-3x}x)+6e^{x^2}x