What is the derivative of x^3e^x-3x^2e^x+6xe^x-6e^x ?

The derivative of x^3e^x-3x^2e^x+6xe^x-6e^x is e^xx^3

What is the first derivative of x^3e^x-3x^2e^x+6xe^x-6e^x ?

The first derivative of x^3e^x-3x^2e^x+6xe^x-6e^x is e^xx^3

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derivative of

x^{3} e^{x} - 3 x^{2} e^{x} + 6 x e^{x} - 6 e^{x}

e^{x} x^{3}

Solution steps

\frac{d}{d x} (x^{3} e^{x} - 3 x^{2} e^{x} + 6 x e^{x} - 6 e^{x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{3} e^{x}) - \frac{d}{d x} (3 x^{2} e^{x}) + \frac{d}{d x} (6 x e^{x}) - \frac{d}{d x} (6 e^{x})

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

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

\frac{d}{d x} (6 x e^{x}) = 6 (e^{x} + e^{x} x)

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

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

Simplify

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

= e^{x} x^{3}

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