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Popular >

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

Solution

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

Solution

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

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 x}

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

Simplify

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

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

Popular Examples

slope ofintercept (3,5),(-2,-20)slope intercept

(3, 5), (- 2, - 20)

derivative of (1-x)^2 derivative of

(1 - x)^{2}

derivative of y=2arcsin(sqrt(3x))derivative of

y = 2 arcsin (3 x)

integral of 24x(6-x^2)^{1/3}

\int 24 x (6 - x^{2})^{\frac{1}{3}} d x

derivative of f(x)=(x+1)e^x derivative of

f (x) = (x + 1) e^{x}

Frequently Asked Questions (FAQ)

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