What is the derivative of ln(arctan(2x^3)) ?

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

What is the first derivative of ln(arctan(2x^3)) ?

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

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derivative of

ln (arctan (2 x^{3}))

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

Solution steps

\frac{d}{d x} (ln (arctan (2 x^{3})))

Apply the chain rule:

\frac{1}{arctan ( 2 x ^{3} )} \frac{d}{d x} (arctan (2 x^{3}))

= \frac{1}{arctan ( 2 x ^{3} )} \frac{d}{d x} (arctan (2 x^{3}))

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

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

Simplify

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

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

\int \frac{3}{x} + 2 e^{x} d x

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

\frac{d}{d x} (\frac{4 - x ^{2}}{4 + x ^{2}})

\int (x + \frac{1}{x ^{4} x}) d x

\int sec^{8} (x) d x

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