What is expand x^{e^x}(e^xln(x)+(e^x)/x) ?

The solution to expand x^{e^x}(e^xln(x)+(e^x)/x) is e^xx^{e^x}ln(x)+e^xx^{e^x-1}

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expand x^{e^x}(e^xln(x)+(e^x)/x)

expand

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

e^{x} x^{e^{x}} ln (x) + e^{x} x^{e^{x} - 1}

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

a = x^{e^{x}}, b = e^{x} ln (x), c = \frac{e ^{x}}{x}

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

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

\frac{e ^{x}}{x} x^{e^{x}} = e^{x} x^{e^{x} - 1}

= e^{x} x^{e^{x}} ln (x) + e^{x} x^{e^{x} - 1}

(e^{t}) (e^{- t} - t e^{- t})

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

lo g_{3} (27)

\frac{( 2 x ^{2} - 4 ) x}{( x + 2 ) ( 10 x ^{2} + 4 x - 5 )}

What is expand x^{e^x}(e^xln(x)+(e^x)/x) ?
The solution to expand x^{e^x}(e^xln(x)+(e^x)/x) is e^xx^{e^x}ln(x)+e^xx^{e^x-1}