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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

derivative of y=e^{-7x^2}derivative of

y = e^{- 7 x^{2}}

derivative of 10^{sqrt(x)}derivative of

1 0^{x}

integral from 0 to pi of e^{-st}sin(t)

\int_{0}^{π} e^{- s t} sin (t) d t

derivative of (cos(x)/(2+sin(x)))

\frac{d}{d x} (\frac{cos ( x )}{2 + sin ( x )})

(dy)/(dx)=e^{4x+2y}

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

Frequently Asked Questions (FAQ)

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