What is the derivative of 2x^2e^{x/2} ?

The derivative of 2x^2e^{x/2} is 4e^{x/2}x+e^{x/2}x^2

What is the first derivative of 2x^2e^{x/2} ?

The first derivative of 2x^2e^{x/2} is 4e^{x/2}x+e^{x/2}x^2

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = e^{\frac{x}{2}}

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

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

\frac{d}{d x} (e^{\frac{x}{2}}) = e^{\frac{x}{2}} \frac{1}{2}

= 2 (2 x e^{\frac{x}{2}} + e^{\frac{x}{2}} \frac{1}{2} x^{2})

Simplify

2 (2 x e^{\frac{x}{2}} + e^{\frac{x}{2}} \frac{1}{2} x^{2}) : 4 e^{\frac{x}{2}} x + e^{\frac{x}{2}} x^{2}

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

\frac{( s - 2 )}{s ^{2} - 2 s + 10}

x \to - 5 lim (\frac{1}{1 + 5})

\frac{d}{d x} ((ln (x))^{2} sin (x))

\frac{d y}{d x} = (x - 3) (y + 1)^{\frac{2}{3}}

\int \frac{4 x}{( 2 x ^{2} - 8 ) ^{5}} d x

What is the derivative of 2x^2e^{x/2} ?
The derivative of 2x^2e^{x/2} is 4e^{x/2}x+e^{x/2}x^2
What is the first derivative of 2x^2e^{x/2} ?
The first derivative of 2x^2e^{x/2} is 4e^{x/2}x+e^{x/2}x^2