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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

derivative of 200x-(x^2)/(30)derivative of

200 x - \frac{x ^{2}}{30}

integral of (x^2-1)e^{x^3-3x-5}

\int (x^{2} - 1) e^{x^{3} - 3 x - 5} d x

tangent of f(x)=(x^2)/(x+4),\at x=3 tangent of

f (x) = \frac{x ^{2}}{x + 4}, at x = 3

derivative of e^{5x^4}

\frac{d}{d x} (e^{5 x^{4}})

(dy)/(dx)+y/x =9x+10

\frac{d y}{d x} + \frac{y}{x} = 9 x + 10

Frequently Asked Questions (FAQ)

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