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

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

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

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

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derivative of

ln (tan (x^{3}))

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (tan (x^{3})) = sec^{2} (x^{3}) \cdot 3 x^{2}

= \frac{1}{tan ( x ^{3} )} sec^{2} (x^{3}) \cdot 3 x^{2}

Simplify

\frac{1}{tan ( x ^{3} )} sec^{2} (x^{3}) \cdot 3 x^{2} : 3 x^{2} sec^{2} (x^{3}) cot (x^{3})

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

\frac{d x}{d t} = - \frac{t}{x}

e^{2 t} sin (4 t)

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

\frac{d}{d x} (x - 6 x)

x \to 1 lim (x^{3})

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