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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

= 2 \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^{'}

= 2 (\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})

= 2 (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}

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

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

\int x sec (x^{2}) tan (x^{2}) d x

f (x) = \frac{2 x ^{3} - 4 x ^{2} + 3}{x}

\frac{\partial}{\partial y} (e^{x} tan (y))

\int 4 x^{- 1} - 4^{x} + 10 e^{2 x} - 8 x d x

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