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

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

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

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

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

3 cot (x)

Solution steps

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

Apply the chain rule:

\frac{1}{sin ^{3} ( x )} \frac{d}{d x} (sin^{3} (x))

= \frac{1}{sin ^{3} ( x )} \frac{d}{d x} (sin^{3} (x))

\frac{d}{d x} (sin^{3} (x)) = 3 sin^{2} (x) cos (x)

= \frac{1}{sin ^{3} ( x )} \cdot 3 sin^{2} (x) cos (x)

Simplify

\frac{1}{sin ^{3} ( x )} \cdot 3 sin^{2} (x) cos (x) : 3 cot (x)

= 3 cot (x)

\int_{- 4}^{12} z + 4 d z

x \to 4 lim (x^{2} + 7 - x)

x^{2} y^{^{''}} - 16 x y^{^{'}} + 72 y = 0

\frac{d}{d x} (\frac{2 x}{x ^{2} + 1})

f (x) = 6 x - x^{2}

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