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

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

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

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

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

e^{x} x^{2} + 4 e^{x} x + 2 e^{x}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

\int \frac{1}{529 + x ^{2}} d x

\frac{d}{d x} (9 ln (x))

11 e^{x}

\int \frac{1}{2} x^{\frac{1}{2}} d x

x \to 4 lim (x^{2} - 3 x + 7)

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