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Popular >

derivative of ln(sqrt(sin(x)))

Solution

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

Solution

\frac{cot ( x )}{2}

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

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

Simplify

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

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

Popular Examples

integral from 3 to infinity of 1/(x^3)

\int_{3}^{\infty} \frac{1}{x ^{3}} d x

integral of 10sin^3(xco)s^2x

\int 10 sin^{3} (x co) s^{2} x d x

(\partial)/(\partial x)(log_{10}(y))

\frac{\partial}{\partial x} (lo g_{10} (y))

derivative of y=3x+8 derivative of

y = 3 x + 8

integral of 2^x5^x

\int 2^{x} 5^{x} d x

Frequently Asked Questions (FAQ)

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