What is the derivative of ln(sin(8x)) ?

The derivative of ln(sin(8x)) is 8cot(8x)

What is the first derivative of ln(sin(8x)) ?

The first derivative of ln(sin(8x)) is 8cot(8x)

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derivative of

ln (sin (8 x))

8 cot (8 x)

Solution steps

\frac{d}{d x} (ln (sin (8 x)))

Apply the chain rule:

\frac{1}{sin ( 8 x )} \frac{d}{d x} (sin (8 x))

= \frac{1}{sin ( 8 x )} \frac{d}{d x} (sin (8 x))

\frac{d}{d x} (sin (8 x)) = cos (8 x) \cdot 8

= \frac{1}{sin ( 8 x )} cos (8 x) \cdot 8

Simplify

\frac{1}{sin ( 8 x )} cos (8 x) \cdot 8 : 8 cot (8 x)

= 8 cot (8 x)

\frac{d ^{2}}{d x ^{2}} (a x^{2} + b x + c)

x \to \infty lim (0. 4^{x})

\frac{d}{d a} (tan (a) csc (a))

g (t) = 1 + ln (t)

f (x) = x^{3}, at x = 4

What is the derivative of ln(sin(8x)) ?
The derivative of ln(sin(8x)) is 8cot(8x)
What is the first derivative of ln(sin(8x)) ?
The first derivative of ln(sin(8x)) is 8cot(8x)