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

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

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

expand

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

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

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

Apply minus-plus rules

+ (- a) = - a

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

Multiply:

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

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

(1, \frac{13}{2}) y (6, - 4)

(2 x + 1) (2 x - 1)

(2 + \frac{1}{4} x)^{8} (2 x - \frac{3}{x})^{2}

(3 - y)^{2}

\frac{\partial}{\partial x} ((z) (x^{2} yz - e^{z}))

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