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Popular >

derivative of (x^2+xe^x)

Solution

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

Solution

e^{x} x^{2} + 3 e^{x} x + e^{x}

Solution steps

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

Apply the Product Rule:

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

f = x^{2} + x, g = e^{x}

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

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

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

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

Simplify

(2 x + 1) e^{x} + e^{x} (x^{2} + x) : e^{x} x^{2} + 3 e^{x} x + e^{x}

= e^{x} x^{2} + 3 e^{x} x + e^{x}

Popular Examples

y^3dx=2x^3dy-2x^2ydx

y^{3} d x = 2 x^{3} d y - 2 x^{2} y d x

integral of sqrt(1+(16)/(9*x^{2/3))}

\int 1 + \frac{16}{9 \cdot x ^{\frac{2}{3}}} d x

integral from 0 to 7 of sqrt(1+9x)

\int_{0}^{7} 1 + 9 x d x

6y^{'''}+3y^{''}=0

6 y^{^{'''}} + 3 y^{^{''}} = 0

tangent of 3/((x+6)),\at x=-4 tangent of

\frac{3}{( x + 6 )}, at x = - 4

Frequently Asked Questions (FAQ)

What is the derivative of (x^2+xe^x) ?
The derivative of (x^2+xe^x) is e^xx^2+3e^xx+e^x
What is the first derivative of (x^2+xe^x) ?
The first derivative of (x^2+xe^x) is e^xx^2+3e^xx+e^x