What is the derivative of ln(2sin(x)) ?

The derivative of ln(2sin(x)) is cot(x)

What is the first derivative of ln(2sin(x)) ?

The first derivative of ln(2sin(x)) is cot(x)

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

cot (x)

Solution steps

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

Apply the chain rule:

\frac{1}{2 sin ( x )} \frac{d}{d x} (2 sin (x))

= \frac{1}{2 sin ( x )} \frac{d}{d x} (2 sin (x))

\frac{d}{d x} (2 sin (x)) = 2 cos (x)

= \frac{1}{2 sin ( x )} \cdot 2 cos (x)

Simplify

\frac{1}{2 sin ( x )} \cdot 2 cos (x) : cot (x)

= cot (x)

y = (3 - e^{x})^{3}

\frac{d y}{d x} = \frac{8 x}{4 y}

f (x) = \frac{3}{x}

\frac{d}{d x} (\frac{π ( 9 x ^{2} + 6 x + 1 )}{36 x})

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

What is the derivative of ln(2sin(x)) ?
The derivative of ln(2sin(x)) is cot(x)
What is the first derivative of ln(2sin(x)) ?
The first derivative of ln(2sin(x)) is cot(x)