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

The derivative of sqrt(x)*(ln(x))^2 is (ln^2(x))/(2sqrt(x))+(2ln(x))/(sqrt(x))

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

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

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derivative of

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

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

Simplify

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

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

\int sin (x) + cos (y) d x

\int \frac{9 - x ^{2}}{( x ^{2} )} d x

\int 2 cos (t) sin (t) d t

\int 4 x - 3 d x

\frac{d}{d x} (\frac{x sinh ( x )}{sinh ( 2 x )})

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