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

The derivative of ln(sin(x^3)) is 3x^2cot(x^3)

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

The first derivative of ln(sin(x^3)) is 3x^2cot(x^3)

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

3 x^{2} cot (x^{3})

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= 3 x^{2} cot (x^{3})

x y = - 121

y = 12 e^{2} x

3 + 7 t + t^{2}

x \to - 8 + lim (\frac{- 9 x}{x + 8})

\frac{d}{d x} (2 x^{2} + 3 x + 2)

What is the derivative of ln(sin(x^3)) ?
The derivative of ln(sin(x^3)) is 3x^2cot(x^3)
What is the first derivative of ln(sin(x^3)) ?
The first derivative of ln(sin(x^3)) is 3x^2cot(x^3)