What is the derivative of 2e^x+4xe^x+x^2e^x ?

The derivative of 2e^x+4xe^x+x^2e^x is 6e^x+6e^xx+e^xx^2

What is the first derivative of 2e^x+4xe^x+x^2e^x ?

The first derivative of 2e^x+4xe^x+x^2e^x is 6e^x+6e^xx+e^xx^2

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\frac{d}{d x} (2 e^{x} + 4 x e^{x} + x^{2} e^{x})

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

Solution steps

\frac{d}{d x} (2 e^{x} + 4 x e^{x} + x^{2} e^{x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (2 e^{x}) + \frac{d}{d x} (4 x e^{x}) + \frac{d}{d x} (x^{2} e^{x})

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

\frac{d}{d x} (4 x e^{x}) = 4 (e^{x} + e^{x} x)

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

= 2 e^{x} + 4 (e^{x} + e^{x} x) + 2 x e^{x} + e^{x} x^{2}

Simplify

2 e^{x} + 4 (e^{x} + e^{x} x) + 2 x e^{x} + e^{x} x^{2} : 6 e^{x} + 6 e^{x} x + e^{x} x^{2}

= 6 e^{x} + 6 e^{x} x + e^{x} x^{2}

\int_{4}^{9} \frac{1}{9 - x} d x

\frac{\partial}{\partial x} (3 x + 8 y + 2)

\frac{\partial}{\partial x} (3 x^{2} - 4 y^{3})

\int_{0}^{\frac{π}{2}} cos (3 x) d x

\int (2 e^{x} + 8 x^{3} + 6 x) d x

What is the derivative of 2e^x+4xe^x+x^2e^x ?
The derivative of 2e^x+4xe^x+x^2e^x is 6e^x+6e^xx+e^xx^2
What is the first derivative of 2e^x+4xe^x+x^2e^x ?
The first derivative of 2e^x+4xe^x+x^2e^x is 6e^x+6e^xx+e^xx^2