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Popular >

derivative of x^2e^x+2xe^x

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

Popular Examples

limit as x approaches infinity of (ln(5))/((1+ln(x)))

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

limit as x approaches 0+of sqrt(x)e^{sin(pi/x)}

x \to 0 + lim (x e^{s i n (\frac{π}{x})})

derivative of ((10+x/pi)^{1/3})

\frac{d}{d x} ((\frac{10 + x}{π})^{\frac{1}{3}})

integral of-1/(1-x)

\int - \frac{1}{1 - x} d x

(\partial)/(\partial x)(z*arctan(y/x))

\frac{\partial}{\partial x} (z \cdot arctan (\frac{y}{x}))

Frequently Asked Questions (FAQ)

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