What is the derivative of log_{e}(sin(x)) ?

The derivative of log_{e}(sin(x)) is cot(x)

What is the first derivative of log_{e}(sin(x)) ?

The first derivative of log_{e}(sin(x)) is cot(x)

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\frac{d}{d x} (lo g_{e} (sin (x)))

cot (x)

Solution steps

\frac{d}{d x} (lo g_{e} (sin (x)))

Simplify

lo g_{e} (sin (x)) : ln (sin (x))

= \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)

x + 2 y = 9, x + 6 = y^{2}

\int sin^{5} (13 x) d x

\int_{0}^{1} π (x^{3} - 1)^{2} d x

f (x) = x^{3} + 4 x, (1, 5)

\frac{d y}{d x} = \frac{x y + y}{x + x y}

What is the derivative of log_{e}(sin(x)) ?
The derivative of log_{e}(sin(x)) is cot(x)
What is the first derivative of log_{e}(sin(x)) ?
The first derivative of log_{e}(sin(x)) is cot(x)