What is the derivative of ln(sin(7x)) ?

The derivative of ln(sin(7x)) is 7cot(7x)

What is the first derivative of ln(sin(7x)) ?

The first derivative of ln(sin(7x)) is 7cot(7x)

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\frac{d}{d x} (ln (sin (7 x)))

7 cot (7 x)

Solution steps

\frac{d}{d x} (ln (sin (7 x)))

Apply the chain rule:

\frac{1}{sin ( 7 x )} \frac{d}{d x} (sin (7 x))

= \frac{1}{sin ( 7 x )} \frac{d}{d x} (sin (7 x))

\frac{d}{d x} (sin (7 x)) = cos (7 x) \cdot 7

= \frac{1}{sin ( 7 x )} cos (7 x) \cdot 7

Simplify

\frac{1}{sin ( 7 x )} cos (7 x) \cdot 7 : 7 cot (7 x)

= 7 cot (7 x)

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

\frac{d y}{d x} = (y + 1)^{- 1}

\frac{d}{d x} (4 e^{x} + \frac{8}{3 x})

x \to 0 lim (ln^{4} (x) x)

t a y l or \frac{1}{1 - x}, 2

What is the derivative of ln(sin(7x)) ?
The derivative of ln(sin(7x)) is 7cot(7x)
What is the first derivative of ln(sin(7x)) ?
The first derivative of ln(sin(7x)) is 7cot(7x)