What is the derivative of x(ln(x)^2) ?

The derivative of x(ln(x)^2) is ln^2(x)+2ln(x)

What is the first derivative of x(ln(x)^2) ?

The first derivative of x(ln(x)^2) is ln^2(x)+2ln(x)

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} ((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)

What is the derivative of x(ln(x)^2) ?
The derivative of x(ln(x)^2) is ln^2(x)+2ln(x)
What is the first derivative of x(ln(x)^2) ?
The first derivative of x(ln(x)^2) is ln^2(x)+2ln(x)