What is the (x(ln(x))^2)^' ?

The (x(ln(x))^2)^' is ln^2(x)+2ln(x)

What is the first (x(ln(x))^2)^' ?

The first (x(ln(x))^2)^' is ln^2(x)+2ln(x)

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(x (ln (x))^{2})^{^{'}}

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

Solution steps

(x (ln (x))^{2})^{'}

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = (ln (x))^{2}

= x^{^{'}} (ln (x))^{2} + ((ln (x))^{2})^{^{'}} x

x^{'} = 1

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

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

Simplify

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

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

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