What is the derivative of ln(sin(11x)) ?

The derivative of ln(sin(11x)) is 11cot(11x)

What is the first derivative of ln(sin(11x)) ?

The first derivative of ln(sin(11x)) is 11cot(11x)

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derivative of

ln (sin (11 x))

11 cot (11 x)

Solution steps

\frac{d}{d x} (ln (sin (11 x)))

Apply the chain rule:

\frac{1}{sin ( 11 x )} \frac{d}{d x} (sin (11 x))

= \frac{1}{sin ( 11 x )} \frac{d}{d x} (sin (11 x))

\frac{d}{d x} (sin (11 x)) = cos (11 x) \cdot 11

= \frac{1}{sin ( 11 x )} cos (11 x) \cdot 11

Simplify

\frac{1}{sin ( 11 x )} cos (11 x) \cdot 11 : 11 cot (11 x)

= 11 cot (11 x)

x \to - 2 lim (x^{2} + 3 x)

t^{2} y^{^{''}} + 9 t y^{^{'}} + 16 y = 0

\int_{1}^{\infty} \frac{1}{x ^{2} + 1} d x

(3 - x)^{^{'}}

2 + 8 x^{\frac{3}{2}}

What is the derivative of ln(sin(11x)) ?
The derivative of ln(sin(11x)) is 11cot(11x)
What is the first derivative of ln(sin(11x)) ?
The first derivative of ln(sin(11x)) is 11cot(11x)