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

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

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

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

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

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

Solution steps

\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^{'}

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

Simplify

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}

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

\frac{d y}{d x} = x (6 - y)

\frac{d}{d x} (\frac{2 x}{1 + 5 x ^{2}})

x y^{^{'}} + 2 y = 4 x

\int e^{- 2 x} + e^{2 x} + 2 d x

\frac{\partial}{\partial v} (2 cos (u))

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