What is the derivative of x^2(e^x) ?

The derivative of x^2(e^x) is 2xe^x+e^xx^2

What is the first derivative of x^2(e^x) ?

The first derivative of x^2(e^x) is 2xe^x+e^xx^2

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

2 x e^{x} + e^{x} x^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

h \to 0 lim (\frac{( 16 + h ) - 4}{h})

\int x (4 + x^{2})^{10} d x

x \to 1 + lim (5 x + 2 p (x))

(x + 3) \frac{d y}{d x} + y = ln (x)

What is the derivative of x^2(e^x) ?
The derivative of x^2(e^x) is 2xe^x+e^xx^2
What is the first derivative of x^2(e^x) ?
The first derivative of x^2(e^x) is 2xe^x+e^xx^2