What is (\partial)/(\partial x)(ln(sin(x))) ?

The answer to (\partial)/(\partial x)(ln(sin(x))) is cot(x)

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(\partial)/(\partial x)(ln(sin(x)))

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

cot (x)

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= cot (x)

\int x^{2} (x^{3} + 1)^{3} d x

\int (x^{2} + x) e^{- 2 x} d x

\frac{d y}{d x} = \frac{x ^{2} - y ^{2}}{x y}, y (2) = 2

4 x, x^{2} - 5

\int se x (x)

What is (\partial)/(\partial x)(ln(sin(x))) ?
The answer to (\partial)/(\partial x)(ln(sin(x))) is cot(x)