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})

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\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})

\frac{d}{d x} (- \frac{2}{( 1 - x ) ^{3}})

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

(t^{2} + \frac{1}{2})^{2}

(x^{2} + 2 y^{2}) d x - x y d y = 0

\frac{\partial}{\partial x} (x e^{\frac{s}{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})