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

The derivative of A(2xe^{2x}+e^{2x}*2x^2) is A(4e^{2x}x^2+8e^{2x}x+2e^{2x})

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

The first derivative of A(2xe^{2x}+e^{2x}*2x^2) is A(4e^{2x}x^2+8e^{2x}x+2e^{2x})

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

A (4 e^{2 x} x^{2} + 8 e^{2 x} x + 2 e^{2 x})

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Expand

2 (e^{2 x} + 2 e^{2 x} x) + 2 (e^{2 x} \cdot 2 x^{2} + 2 x e^{2 x}) : 4 e^{2 x} x^{2} + 8 e^{2 x} x + 2 e^{2 x}

= A (4 e^{2 x} x^{2} + 8 e^{2 x} x + 2 e^{2 x})

What is the derivative of A(2xe^{2x}+e^{2x}*2x^2) ?
The derivative of A(2xe^{2x}+e^{2x}*2x^2) is A(4e^{2x}x^2+8e^{2x}x+2e^{2x})
What is the first derivative of A(2xe^{2x}+e^{2x}*2x^2) ?
The first derivative of A(2xe^{2x}+e^{2x}*2x^2) is A(4e^{2x}x^2+8e^{2x}x+2e^{2x})