What is the derivative of f(x)=x^2e^{2x} ?

The derivative of f(x)=x^2e^{2x} is 2xe^{2x}+e^{2x}*2x^2

What is the first derivative of f(x)=x^2e^{2x} ?

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

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derivative of

f (x) = x^{2} 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}

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

\frac{d y}{d t} = 9 t y^{2}

\int \frac{x + 4}{x + 1} d x

\int (\frac{1}{x ( 1 + ln ( x ) )}) d x

\frac{d}{d x} (e^{- x} cos (x))

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