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

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

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

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

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

2 x e^{2 x} + e^{2 x} \cdot 2 x^{2}

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = e^{2 x}

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

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

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

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

\int \frac{2 ^{2 x}}{1 + 2 ^{2 x}} d x

t \frac{d y}{d t} + 4 y = t^{2}

x y^{2} y^{^{'}} = y^{3} - 5 x^{3}, y (1) = 2

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

sin (x) + \frac{4}{5} cot (x)

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