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

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

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

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

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derivative of

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

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

Solution steps

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

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})

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

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

Simplify

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

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

x \to 0 lim (4 x^{2} - 2 x - 6)

x^{x^{3}}

f (x) =, 4 at x

\frac{d}{d y} (6 y^{2})

\frac{d}{d x} (x + 3 y^{\frac{1}{3}})

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