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})

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

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

im pl i c i t \frac{d y}{d x}, 3 x^{2} y^{3} = 3 x - 2 y^{2} - 16

d er i v a t i v e (x - 3)^{\frac{2}{3}}

y^{^{'}} = \frac{6 x}{y}

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)