What is the derivative of 6x^3e^x ?

The derivative of 6x^3e^x is 6(3x^2e^x+e^xx^3)

What is the first derivative of 6x^3e^x ?

The first derivative of 6x^3e^x is 6(3x^2e^x+e^xx^3)

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\frac{d}{d x} (6 x^{3} e^{x})

6 (3 x^{2} e^{x} + e^{x} x^{3})

Solution steps

\frac{d}{d x} (6 x^{3} e^{x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \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}

= 6 (\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}

= 6 (3 x^{2} e^{x} + e^{x} x^{3})

What is the derivative of 6x^3e^x ?
The derivative of 6x^3e^x is 6(3x^2e^x+e^xx^3)
What is the first derivative of 6x^3e^x ?
The first derivative of 6x^3e^x is 6(3x^2e^x+e^xx^3)