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Popular >

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

Solution

derivative of

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

Solution

e^{x} x^{2}

Solution steps

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

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

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

Simplify

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

= e^{x} x^{2}

Popular Examples

y^{''}-10y^'+26y=4

y^{^{''}} - 10 y^{^{'}} + 26 y = 4

integral of 4/(4x^2+4x+65)

\int \frac{4}{4 x ^{2} + 4 x + 65} d x

integral from 0 to 2 of sqrt(9x+19)

\int_{0}^{2} 9 x + 19 d x

(dy)/(dx)(x^2+1)+7x(y-1)=0,y(0)=4

\frac{d y}{d x} (x^{2} + 1) + 7 x (y - 1) = 0, y (0) = 4

integral of (x^2)/(sqrt(x^2+9))

\int \frac{x ^{2}}{x ^{2} + 9} d x

Frequently Asked Questions (FAQ)

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