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Popular >

derivative of ln(sin(x/2))

Solution

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

Solution

\frac{cot ( \frac{x}{2} )}{2}

Solution steps

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

Apply the chain rule:

\frac{1}{sin ( \frac{x}{2} )} \frac{d}{d x} (sin (\frac{x}{2}))

= \frac{1}{sin ( \frac{x}{2} )} \frac{d}{d x} (sin (\frac{x}{2}))

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

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

Simplify

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

= \frac{cot ( \frac{x}{2} )}{2}

Graph

Popular Examples

integral of (3^{5x-2})

\int (3^{5 x - 2}) d x

integral from-1 to 3 of 3xe^{2x^2-5}

\int_{- 1}^{3} 3 x e^{2 x^{2} - 5} d x

limit as x approaches 1 of (\sqrt[3]{x+7}-2)/(x^3-1)

x \to 1 lim (\frac{3 x + 7 - 2}{x ^{3} - 1})

integral of sqrt(x)+x

\int x + x d x

derivative of ((6x^2-5)/(4-x))^3 derivative of

(\frac{6 x ^{2} - 5}{4 - x})^{3}

Frequently Asked Questions (FAQ)

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