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

The derivative of 4e^{x^2}x^3+6e^{x^2}x is 8e^{x^2}x^4+24e^{x^2}x^2+6e^{x^2}

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

The first derivative of 4e^{x^2}x^3+6e^{x^2}x is 8e^{x^2}x^4+24e^{x^2}x^2+6e^{x^2}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

8 e^{x^{2}} x^{4} + 24 e^{x^{2}} x^{2} + 6 e^{x^{2}}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (4 e^{x^{2}} x^{3}) = 4 (2 e^{x^{2}} x^{4} + 3 e^{x^{2}} x^{2})

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

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

Simplify

4 (2 e^{x^{2}} x^{4} + 3 e^{x^{2}} x^{2}) + 6 (2 e^{x^{2}} x^{2} + e^{x^{2}}) : 8 e^{x^{2}} x^{4} + 24 e^{x^{2}} x^{2} + 6 e^{x^{2}}

= 8 e^{x^{2}} x^{4} + 24 e^{x^{2}} x^{2} + 6 e^{x^{2}}

\int_{0}^{100} e^{- \frac{x}{0.033}} d x

f (x) = (x^{3} - 2)^{3}

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

3 x^{2} + 3 x - 8, 2 x^{2} + x + 7

(3^{x})^{^{'}}

What is the derivative of 4e^{x^2}x^3+6e^{x^2}x ?
The derivative of 4e^{x^2}x^3+6e^{x^2}x is 8e^{x^2}x^4+24e^{x^2}x^2+6e^{x^2}
What is the first derivative of 4e^{x^2}x^3+6e^{x^2}x ?
The first derivative of 4e^{x^2}x^3+6e^{x^2}x is 8e^{x^2}x^4+24e^{x^2}x^2+6e^{x^2}