What is (xlog_{10}(x)-x)(1/(4x^2)-x/4) ?

The solution to (xlog_{10}(x)-x)(1/(4x^2)-x/4) is ((log_{10}(x)-1)(1-x^3))/(4x)

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simplify (xlog_{10}(x)-x)(1/(4x^2)-x/4)

simplify

(x lo g_{10} (x) - x) (\frac{1}{4 x ^{2}} - \frac{x}{4})

\frac{( lo g _{10} ( x ) - 1 ) ( 1 - x ^{3} )}{4 x}

Solution steps

(x lo g_{10} (x) - x) (\frac{1}{4 x ^{2}} - \frac{x}{4})

Join

\frac{1}{4 x ^{2}} - \frac{x}{4} : \frac{1 - x ^{3}}{4 x ^{2}}

= (x lo g_{10} (x) - x) \frac{1 - x ^{3}}{4 x ^{2}}

Apply the fraction rule:

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

= \frac{( x lo g _{10} ( x ) - x ) ( 1 - x ^{3} )}{4 x ^{2}}

Factor out common term

x : x (lo g_{10} (x) - 1)

= \frac{x ( lo g _{10} ( x ) - 1 ) ( 1 - x ^{3} )}{4 x ^{2}}

Apply exponent rule:

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

x^{2} = xx

= \frac{x ( lo g _{10} ( x ) - 1 ) ( 1 - x ^{3} )}{4 xx}

Cancel the common factor:

x

= \frac{( lo g _{10} ( x ) - 1 ) ( 1 - x ^{3} )}{4 x}

\frac{\partial}{\partial v} ((z) (2 u^{2} + 2 v^{2})^{2})

x - 2 \cdot (x^{2} - 2)

(x + 1) (x - 3) (x + 3)

(x - 22) (x + 22)

(- 8 M + 38) (\frac{2}{5})

What is (xlog_{10}(x)-x)(1/(4x^2)-x/4) ?
The solution to (xlog_{10}(x)-x)(1/(4x^2)-x/4) is ((log_{10}(x)-1)(1-x^3))/(4x)