What is the derivative of 2(2e^{x^2}x^2+e^{x^2}) ?

The derivative of 2(2e^{x^2}x^2+e^{x^2}) is 2(4e^{x^2}x^3+6e^{x^2}x)

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

The first derivative of 2(2e^{x^2}x^2+e^{x^2}) is 2(4e^{x^2}x^3+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

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

2 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= 2 (2 (2 e^{x^{2}} x^{3} + 2 e^{x^{2}} x) + e^{x^{2}} \cdot 2 x)

Expand

2 (2 e^{x^{2}} x^{3} + 2 e^{x^{2}} x) + e^{x^{2}} \cdot 2 x : 4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x

= 2 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)

What is the derivative of 2(2e^{x^2}x^2+e^{x^2}) ?
The derivative of 2(2e^{x^2}x^2+e^{x^2}) is 2(4e^{x^2}x^3+6e^{x^2}x)
What is the first derivative of 2(2e^{x^2}x^2+e^{x^2}) ?
The first derivative of 2(2e^{x^2}x^2+e^{x^2}) is 2(4e^{x^2}x^3+6e^{x^2}x)