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

The derivative of (ln(x)^2(sin(x))) is (2ln(x)sin(x))/x+ln^2(x)cos(x)

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

\frac{d}{d x} (sin (x)) = cos (x)

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

Multiply fractions:

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

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

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