What is the derivative of 3ln(sin(x)) ?

The derivative of 3ln(sin(x)) is 3cot(x)

What is the first derivative of 3ln(sin(x)) ?

The first derivative of 3ln(sin(x)) is 3cot(x)

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\frac{d}{d x} (3 ln (sin (x)))

3 cot (x)

Solution steps

\frac{d}{d x} (3 ln (sin (x)))

Take the constant out:

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

= 3 \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)

= 3 \cdot \frac{1}{sin ( x )} cos (x)

Simplify

3 \cdot \frac{1}{sin ( x )} cos (x) : 3 cot (x)

= 3 cot (x)

What is the derivative of 3ln(sin(x)) ?
The derivative of 3ln(sin(x)) is 3cot(x)
What is the first derivative of 3ln(sin(x)) ?
The first derivative of 3ln(sin(x)) is 3cot(x)