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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

= 3 \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}

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

\int 2 ln (x^{x}) d x

\frac{\partial}{\partial z} (0)

\frac{d}{d x} (x^{7 s i n (x)})

\frac{d}{d u} (u^{2} + v^{2})

\frac{3 e ^{x}}{2 e ^{x} - 7}

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