What is e^x*1/3 e^{-x}xln(x) ?

The solution to e^x*1/3 e^{-x}xln(x) is (xln(x))/3

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simplify e^x*1/3 e^{-x}xln(x)

simplify

e^{x} \cdot \frac{1}{3} e^{- x} x ln (x)

\frac{x ln ( x )}{3}

Solution steps

e^{x} \frac{1}{3} e^{- x} x ln (x)

Apply exponent rule:

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

e^{x} e^{- x} = e^{x - x}

= \frac{1}{3} e^{x - x} x ln (x)

Add similar elements:

x - x = 0

= \frac{1}{3} e^{0} x ln (x)

Apply rule

a^{0} = 1, a \neq = 0

e^{0} = 1

= 1 \cdot \frac{1}{3} x ln (x)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 1 \cdot \frac{1 \cdot x}{3} ln (x)

Refine

= \frac{x}{3} ln (x)

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{x ln ( x )}{3}

\frac{( 3 \cdot 1 0 ^{8} )}{1.177 \cdot 1 0 ^{- 7}} \cdot 6.63 \cdot 1 0^{- 34}

(\frac{2 e ^{- 4}}{6})^{- 3}

3.28 \cdot 1 0^{- 12}

5 t e^{- s t} H (t)

1 (1) (0.3)^{10}

What is e^x*1/3 e^{-x}xln(x) ?
The solution to e^x*1/3 e^{-x}xln(x) is (xln(x))/3