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

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

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

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

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

- 2 cot (x)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - 2 \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)

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

Simplify

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

= - 2 cot (x)

\int \frac{1}{x ^{2} + 2 x + 82} d x

(x^{2} - 2 y^{2}) d x + x y d y = 0

\frac{d}{d x} ((\frac{1}{3})^{2})

y^{^{'''}} - 6 y^{^{''}} = 3 - cos (x)

\frac{\partial}{\partial y} (y x^{2} + y^{2})

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