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

The derivative of e^x*x^2 is e^xx^2+2xe^x

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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