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Popular Calculus >

derivative of xe^xln(x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = e^{x} ln (x)

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

\frac{d x}{d x} = 1

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

= 1 \cdot e^{x} ln (x) + (e^{x} ln (x) + \frac{e ^{x}}{x}) x

Simplify

1 \cdot e^{x} ln (x) + (e^{x} ln (x) + \frac{e ^{x}}{x}) x : e^{x} ln (x) + e^{x} x ln (x) + e^{x}

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

Graph

Popular Examples

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x \to 0 lim (\frac{x ^{2} - 1}{x ^{2}})

Frequently Asked Questions (FAQ)

What is the derivative of xe^xln(x) ?
The derivative of xe^xln(x) is e^xln(x)+e^xxln(x)+e^x
What is the first derivative of xe^xln(x) ?
The first derivative of xe^xln(x) is e^xln(x)+e^xxln(x)+e^x