What is the derivative of y=x^3e^x ?

The derivative of y=x^3e^x is 3x^2e^x+e^xx^3

What is the first derivative of y=x^3e^x ?

The first derivative of y=x^3e^x is 3x^2e^x+e^xx^3

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derivative

3 x^{2} e^{x} + e^{x} x^{3}

Solution steps

\frac{d}{d x} (x^{3} e^{x})

Apply the Product Rule:

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

f = x^{3}, g = e^{x}

= \frac{d}{d x} (x^{3}) e^{x} + \frac{d}{d x} (e^{x}) x^{3}

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

= 3 x^{2} e^{x} + e^{x} x^{3}

What is the derivative of y=x^3e^x ?
The derivative of y=x^3e^x is 3x^2e^x+e^xx^3
What is the first derivative of y=x^3e^x ?
The first derivative of y=x^3e^x is 3x^2e^x+e^xx^3