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

The derivative of 3x^2e^x+e^x(x^3+2) is e^xx^3+6e^xx^2+6e^xx+2e^x

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

The first derivative of 3x^2e^x+e^x(x^3+2) is e^xx^3+6e^xx^2+6e^xx+2e^x

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derivative of

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d x} (x \frac{1}{2})

\int_{1}^{8} 3 x - \frac{1}{x} d x

\int \frac{1}{2 ( x + 1 )} d x

f (x) = x - x

\int \frac{( x + 7 )}{x ^{2} + 9} d x

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