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

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

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

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

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

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

Solution steps

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

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}

\frac{3 x}{9 x ^{2} + 4 x - 9}

x \to 1 lim (\frac{[ x ]}{∣ x ∣})

x \to π lim (sin (6 x))

x (3 x + 4)^{2}

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