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

The derivative of ln^2(sin(2x)) is 4ln(sin(2x))cot(2x)

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

The first derivative of ln^2(sin(2x)) is 4ln(sin(2x))cot(2x)

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

4 ln (sin (2 x)) cot (2 x)

Solution steps

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

Apply the chain rule:

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

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

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

= 2 ln (sin (2 x)) \cdot 2 cot (2 x)

Simplify

= 4 ln (sin (2 x)) cot (2 x)

What is the derivative of ln^2(sin(2x)) ?
The derivative of ln^2(sin(2x)) is 4ln(sin(2x))cot(2x)
What is the first derivative of ln^2(sin(2x)) ?
The first derivative of ln^2(sin(2x)) is 4ln(sin(2x))cot(2x)