What is (e^{1/2 x}ln(x))(xe^{1/2 x}) ?

The solution to (e^{1/2 x}ln(x))(xe^{1/2 x}) is e^xxln(x)

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simplify (e^{1/2 x}ln(x))(xe^{1/2 x})

simplify

(e^{\frac{1}{2} x} ln (x)) (x e^{\frac{1}{2} x})

e^{x} x ln (x)

Solution steps

(e^{\frac{1}{2} x} ln (x)) (x e^{\frac{1}{2} x})

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{\frac{1}{2} x} e^{\frac{1}{2} x} = e^{\frac{1}{2} x + \frac{1}{2} x}

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

e^{\frac{1}{2} x + \frac{1}{2} x} = e^{x}

= e^{x} x ln (x)

120 π \cdot 5 \cdot 1 0^{- 3}

24 x^{2} (a - x)^{2}

2 \cdot 3.14 \cdot (6.67 \cdot 1 0^{- 6}) \cdot 150 (2.67 - 1.17)

0.2 \cdot 7.238 \cdot 1 0^{- 15}

What is (e^{1/2 x}ln(x))(xe^{1/2 x}) ?
The solution to (e^{1/2 x}ln(x))(xe^{1/2 x}) is e^xxln(x)