What is the derivative of ln(sin(10x)) ?

The derivative of ln(sin(10x)) is 10cot(10x)

What is the first derivative of ln(sin(10x)) ?

The first derivative of ln(sin(10x)) is 10cot(10x)

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\frac{d}{d x} (ln (sin (10 x)))

10 cot (10 x)

Solution steps

\frac{d}{d x} (ln (sin (10 x)))

Apply the chain rule:

\frac{1}{sin ( 10 x )} \frac{d}{d x} (sin (10 x))

= \frac{1}{sin ( 10 x )} \frac{d}{d x} (sin (10 x))

\frac{d}{d x} (sin (10 x)) = cos (10 x) \cdot 10

= \frac{1}{sin ( 10 x )} cos (10 x) \cdot 10

Simplify

\frac{1}{sin ( 10 x )} cos (10 x) \cdot 10 : 10 cot (10 x)

= 10 cot (10 x)

y^{^{''}} + 6 y^{^{'}} - 16 y = - 272 sin (8 x)

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

\frac{d}{d x} (2 x e^{- 4 x})

y = sin (3 x) + cos (8 x)

\frac{d}{d x} (cos (3 x))

What is the derivative of ln(sin(10x)) ?
The derivative of ln(sin(10x)) is 10cot(10x)
What is the first derivative of ln(sin(10x)) ?
The first derivative of ln(sin(10x)) is 10cot(10x)