What is the derivative of-5ln(sin(x)) ?

The derivative of-5ln(sin(x)) is -5cot(x)

What is the first derivative of-5ln(sin(x)) ?

The first derivative of-5ln(sin(x)) is -5cot(x)

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derivative of

- 5 ln (sin (x))

- 5 cot (x)

Solution steps

\frac{d}{d x} (- 5 ln (sin (x)))

Take the constant out:

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

= - 5 \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)

= - 5 \cdot \frac{1}{sin ( x )} cos (x)

Simplify

- 5 \cdot \frac{1}{sin ( x )} cos (x) : - 5 cot (x)

= - 5 cot (x)

\int \frac{4}{9 - 9 x ^{2}} d x

x^{2} + 9 (- 5.34)

x \to 0 lim (3 x^{2} - 2 x + 4)

\frac{d}{d x} (15 x^{5} - \frac{60}{7 x ^{6}} - 1)

\int \frac{r}{( r ^{2} + z ^{2} ) ^{\frac{3}{2}}} d r

What is the derivative of-5ln(sin(x)) ?
The derivative of-5ln(sin(x)) is -5cot(x)
What is the first derivative of-5ln(sin(x)) ?
The first derivative of-5ln(sin(x)) is -5cot(x)