What is the derivative of y=ln(sin(x)) ?

The derivative of y=ln(sin(x)) is cot(x)

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

The first derivative of y=ln(sin(x)) is cot(x)

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derivative of

y = ln (sin (x))

cot (x)

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= cot (x)

\frac{d}{d x} (x^{2} 7 x - 5)

\frac{d}{d x} (∣ x - 9 ∣)

y^{^{''}} - 2 y^{^{'}} + 37 y = 0

x \to 0 + lim (\frac{x ^{x} - 1}{x})

\frac{d y}{d x} = sec (x) + y tan (x)

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