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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

\int a sin (x) d x

\frac{d}{d x} (cos (x^{2} + y^{2}))

a re a y^{2} = 4 x, y = 2 x + 4

y^{^{''}} + 9 y = - 30 sin (3 t)

\frac{d}{d x} (ln (sec (x) - tan (x)))

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