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

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

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

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

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derivative of

f (x) = 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)

6 x + 10 y = 8

(4, 4)

f (x) = cos (x^{3})

f (x) = - 2 x + 5

f (x) = - 3 x^{2} - 6 x, at x = - 1

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