What is the derivative of ln(sin(3x)) ?

The derivative of ln(sin(3x)) is 3cot(3x)

What is the first derivative of ln(sin(3x)) ?

The first derivative of ln(sin(3x)) is 3cot(3x)

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\frac{d}{d x} (ln (sin (3 x)))

3 cot (3 x)

Solution steps

\frac{d}{d x} (ln (sin (3 x)))

Apply the chain rule:

\frac{1}{sin ( 3 x )} \frac{d}{d x} (sin (3 x))

= \frac{1}{sin ( 3 x )} \frac{d}{d x} (sin (3 x))

\frac{d}{d x} (sin (3 x)) = cos (3 x) \cdot 3

= \frac{1}{sin ( 3 x )} cos (3 x) \cdot 3

Simplify

\frac{1}{sin ( 3 x )} cos (3 x) \cdot 3 : 3 cot (3 x)

= 3 cot (3 x)

\frac{d}{d x} (x^{\frac{2}{3}} - x^{\frac{1}{3}} + 4)

\frac{d}{d y} (- y)

\int x e^{12 x} d x

\frac{\partial}{\partial x} (- 4 x)

\int \frac{1}{2 x - 5} d x

What is the derivative of ln(sin(3x)) ?
The derivative of ln(sin(3x)) is 3cot(3x)
What is the first derivative of ln(sin(3x)) ?
The first derivative of ln(sin(3x)) is 3cot(3x)