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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

4 x^{3} - 12 x^{2}

\frac{d}{d x} (e^{7 x - 4})

\int 3 sin^{2} (4 x) d x

\frac{d y}{d x} = 2 (x + 1) - y

\frac{d}{d x} (- \frac{18}{x ^{3}} + \frac{3}{x ^{2}})

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