What is expand x^{3/2}(1-(1/2)ln(x)) ?

The solution to expand x^{3/2}(1-(1/2)ln(x)) is x^{3/2}-(x^{3/2}ln(x))/2

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expand x^{3/2}(1-(1/2)ln(x))

expand

x^{\frac{3}{2}} (1 - (\frac{1}{2}) ln (x))

x^{\frac{3}{2}} - \frac{x ^{\frac{3}{2}} ln ( x )}{2}

Solution steps

x^{\frac{3}{2}} (1 - (\frac{1}{2}) ln (x))

Apply the distributive law:

a (b - c) = ab - a c

a = x^{\frac{3}{2}}, b = 1, c = (\frac{1}{2}) ln (x)

= x^{\frac{3}{2}} \cdot 1 - x^{\frac{3}{2}} (\frac{1}{2}) ln (x)

= 1 \cdot x^{\frac{3}{2}} - (\frac{1}{2}) x^{\frac{3}{2}} ln (x)

Simplify

1 \cdot x^{\frac{3}{2}} - (\frac{1}{2}) x^{\frac{3}{2}} ln (x) : x^{\frac{3}{2}} - \frac{x ^{\frac{3}{2}} ln ( x )}{2}

= x^{\frac{3}{2}} - \frac{x ^{\frac{3}{2}} ln ( x )}{2}

\frac{\partial}{\partial y} ((z) (2 - 2 x - 4 y))

\frac{y ^{2} ( - y ^{2} + 1 )}{2}

\frac{\partial}{\partial x} ((f (x, y)) (4 x - 2 y^{4}))

\frac{33 x ^{2}}{10} - \frac{6 x ^{2}}{5}

\frac{x ( 2 x + 3 )}{x + 1}

What is expand x^{3/2}(1-(1/2)ln(x)) ?
The solution to expand x^{3/2}(1-(1/2)ln(x)) is x^{3/2}-(x^{3/2}ln(x))/2