What is the derivative of 14(4e^{x^2}x^3+6e^{x^2}x) ?

The derivative of 14(4e^{x^2}x^3+6e^{x^2}x) is 14(8e^{x^2}x^4+24e^{x^2}x^2+6e^{x^2})

What is the first derivative of 14(4e^{x^2}x^3+6e^{x^2}x) ?

The first derivative of 14(4e^{x^2}x^3+6e^{x^2}x) is 14(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

14 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)

14 (8 e^{x^{2}} x^{4} + 24 e^{x^{2}} x^{2} + 6 e^{x^{2}})

Solution steps

\frac{d}{d x} (14 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x))

Take the constant out:

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

= 14 \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^{'}

= 14 (\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}})

= 14 (4 (2 e^{x^{2}} x^{4} + 3 e^{x^{2}} x^{2}) + 6 (2 e^{x^{2}} x^{2} + e^{x^{2}}))

Expand

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}}

= 14 (8 e^{x^{2}} x^{4} + 24 e^{x^{2}} x^{2} + 6 e^{x^{2}})

(x + 7) \cdot ln (x)

\frac{1}{ln ( x )}

x \to 3 lim (4 - x^{2})

\frac{d}{d x} (2 x + \frac{8}{x})

\frac{\partial}{\partial y} (x + 2 y - 22)

What is the derivative of 14(4e^{x^2}x^3+6e^{x^2}x) ?
The derivative of 14(4e^{x^2}x^3+6e^{x^2}x) is 14(8e^{x^2}x^4+24e^{x^2}x^2+6e^{x^2})
What is the first derivative of 14(4e^{x^2}x^3+6e^{x^2}x) ?
The first derivative of 14(4e^{x^2}x^3+6e^{x^2}x) is 14(8e^{x^2}x^4+24e^{x^2}x^2+6e^{x^2})