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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

2 sin (ln (x)) \frac{cos ( ln ( x ) )}{x} : \frac{sin ( 2 ln ( x ) )}{x}

= \frac{sin ( 2 ln ( x ) )}{x}

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