What is the derivative of ln(arctan(4x^3)) ?

The derivative of ln(arctan(4x^3)) is (12x^2)/(arctan(4x^3)(16x^6+1))

What is the first derivative of ln(arctan(4x^3)) ?

The first derivative of ln(arctan(4x^3)) is (12x^2)/(arctan(4x^3)(16x^6+1))

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\frac{d}{d x} (ln (arctan (4 x^{3})))

\frac{12 x ^{2}}{arctan ( 4 x ^{3} ) ( 16 x ^{6} + 1 )}

Solution steps

\frac{d}{d x} (ln (arctan (4 x^{3})))

Apply the chain rule:

\frac{1}{arctan ( 4 x ^{3} )} \frac{d}{d x} (arctan (4 x^{3}))

= \frac{1}{arctan ( 4 x ^{3} )} \frac{d}{d x} (arctan (4 x^{3}))

\frac{d}{d x} (arctan (4 x^{3})) = \frac{12 x ^{2}}{16 x ^{6} + 1}

= \frac{1}{arctan ( 4 x ^{3} )} \cdot \frac{12 x ^{2}}{16 x ^{6} + 1}

Simplify

\frac{1}{arctan ( 4 x ^{3} )} \cdot \frac{12 x ^{2}}{16 x ^{6} + 1} : \frac{12 x ^{2}}{arctan ( 4 x ^{3} ) ( 16 x ^{6} + 1 )}

= \frac{12 x ^{2}}{arctan ( 4 x ^{3} ) ( 16 x ^{6} + 1 )}

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What is the derivative of ln(arctan(4x^3)) ?
The derivative of ln(arctan(4x^3)) is (12x^2)/(arctan(4x^3)(16x^6+1))
What is the first derivative of ln(arctan(4x^3)) ?
The first derivative of ln(arctan(4x^3)) is (12x^2)/(arctan(4x^3)(16x^6+1))