What is expand x^{(1-2x)/x}*(1-ln(x)) ?

The solution to expand x^{(1-2x)/x}*(1-ln(x)) is x^{(1-2x)/x}-x^{(1-2x)/x}ln(x)

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expand x^{(1-2x)/x}*(1-ln(x))

expand

x^{\frac{1 - 2 x}{x}} \cdot (1 - ln (x))

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

Solution steps

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

Apply the distributive law:

a (b - c) = ab - a c

a = x^{\frac{1 - 2 x}{x}}, b = 1, c = ln (x)

= x^{\frac{1 - 2 x}{x}} \cdot 1 - x^{\frac{1 - 2 x}{x}} ln (x)

= 1 \cdot x^{\frac{1 - 2 x}{x}} - x^{\frac{1 - 2 x}{x}} ln (x)

Multiply:

1 \cdot x^{\frac{1 - 2 x}{x}} = x^{\frac{1 - 2 x}{x}}

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

(y - x + x y cot (x)) d x + x d y_{= 0}

\frac{d}{d t} ((z (t)) (- 10 sin (t) + 2 cos (t)))

\frac{( 2 n - 1 ) ( 2 n )}{2} n

(s + 2 π)^{2}

\frac{d}{d r} ((r) (\frac{8 π r}{3} - \frac{2 v}{r}))

What is expand x^{(1-2x)/x}*(1-ln(x)) ?
The solution to expand x^{(1-2x)/x}*(1-ln(x)) is x^{(1-2x)/x}-x^{(1-2x)/x}ln(x)