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

The derivative of log_{sqrt(e)}(sin(x)) is 2cot(x)

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

The first derivative of log_{sqrt(e)}(sin(x)) is 2cot(x)

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

2 cot (x)

Solution steps

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

Simplify

lo g_{e} (sin (x)) : 2 ln (sin (x))

= \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)

t (t cos (t) - sin (t))

n = 1 \sum \infty \frac{- 1 ^{n}}{n}

x \to 2 lim (\frac{x ^{2} - 3 x + 2}{x ^{2} + 5 x - 14})

t^{2} \cdot e^{- 4 t}

\int sin^{4} (x) cos^{2} (x) d x

What is the derivative of log_{sqrt(e)}(sin(x)) ?
The derivative of log_{sqrt(e)}(sin(x)) is 2cot(x)
What is the first derivative of log_{sqrt(e)}(sin(x)) ?
The first derivative of log_{sqrt(e)}(sin(x)) is 2cot(x)