What is the derivative of 2x^3e^x ?

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

What is the first derivative of 2x^3e^x ?

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

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

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

Solution steps

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

Take the constant out:

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

= 2 \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}

= 2 (\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}

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

\frac{3}{x}

f (x) = x^{3} - 2 x + 1

- 3 sin (2 t)

\int x^{\frac{3}{2}} + 2 x + 1 d x

x y^{^{'}} + y = 32 x

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