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

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

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expand ln^{x^2}(x)(2xln(ln(x))+x/(ln(x)))

expand

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

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

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

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

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

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

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

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

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

(4 - y i)^{2}

(270 + 905) c m^{3}

(x - \frac{5}{2})^{2}

(2 + cos (x))^{2}

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