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Popular >

derivative of (x^2+2xe^x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

integral from-1 to 1 of cos(npix)

\int_{- 1}^{1} cos (nπ x) d x

tangent of x^2+2xy-y^2+x=51,(5,7)tangent of

x^{2} + 2 x y - y^{2} + x = 51, (5, 7)

slope of (4.3)(4.6)slope

(4.3) (4.6)

integral of e^{-x}+e^{-3x}

\int e^{- x} + e^{- 3 x} d x

sum from n=0 to infinity of (n!)/(n^n)

n = 0 \sum \infty \frac{n !}{n ^{n}}

Frequently Asked Questions (FAQ)

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