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

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

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

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

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

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

Solution steps

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

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

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

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

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

Simplify

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

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

\int 7 e^{x} 3 + e^{x} d x

\int r^{5} d r

x \to 0 lim (cosh (x))

\frac{d x}{d t} = 1 - 3 x, x (1) = - 2

\frac{d y}{d x} = (\frac{x}{1 - 6 x ^{2}})

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