What is the derivative of ln(sin(6x)) ?

The derivative of ln(sin(6x)) is 6cot(6x)

What is the first derivative of ln(sin(6x)) ?

The first derivative of ln(sin(6x)) is 6cot(6x)

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\frac{d}{d x} (ln (sin (6 x)))

6 cot (6 x)

Solution steps

\frac{d}{d x} (ln (sin (6 x)))

Apply the chain rule:

\frac{1}{sin ( 6 x )} \frac{d}{d x} (sin (6 x))

= \frac{1}{sin ( 6 x )} \frac{d}{d x} (sin (6 x))

\frac{d}{d x} (sin (6 x)) = cos (6 x) \cdot 6

= \frac{1}{sin ( 6 x )} cos (6 x) \cdot 6

Simplify

\frac{1}{sin ( 6 x )} cos (6 x) \cdot 6 : 6 cot (6 x)

= 6 cot (6 x)

(- 6, 6), (4, - 7)

3 y^{^{''}} = 2 y^{^{'}}

\int cos (x^{2}) d x

\int \frac{x ^{2}}{x ^{2} + 8} d x

\int s 9^{s} d s

What is the derivative of ln(sin(6x)) ?
The derivative of ln(sin(6x)) is 6cot(6x)
What is the first derivative of ln(sin(6x)) ?
The first derivative of ln(sin(6x)) is 6cot(6x)