What is the derivative of ln(arctan(8x^3)) ?

The derivative of ln(arctan(8x^3)) is (24x^2)/(arctan(8x^3)(64x^6+1))

What is the first derivative of ln(arctan(8x^3)) ?

The first derivative of ln(arctan(8x^3)) is (24x^2)/(arctan(8x^3)(64x^6+1))

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\frac{d}{d x} (ln (arctan (8 x^{3})))

\frac{24 x ^{2}}{arctan ( 8 x ^{3} ) ( 64 x ^{6} + 1 )}

Solution steps

\frac{d}{d x} (ln (arctan (8 x^{3})))

Apply the chain rule:

\frac{1}{arctan ( 8 x ^{3} )} \frac{d}{d x} (arctan (8 x^{3}))

= \frac{1}{arctan ( 8 x ^{3} )} \frac{d}{d x} (arctan (8 x^{3}))

\frac{d}{d x} (arctan (8 x^{3})) = \frac{24 x ^{2}}{64 x ^{6} + 1}

= \frac{1}{arctan ( 8 x ^{3} )} \cdot \frac{24 x ^{2}}{64 x ^{6} + 1}

Simplify

\frac{1}{arctan ( 8 x ^{3} )} \cdot \frac{24 x ^{2}}{64 x ^{6} + 1} : \frac{24 x ^{2}}{arctan ( 8 x ^{3} ) ( 64 x ^{6} + 1 )}

= \frac{24 x ^{2}}{arctan ( 8 x ^{3} ) ( 64 x ^{6} + 1 )}

\int 4 e^{9 x} d x

f (x) = x^{4} - 25 x^{2} + 144, at x = 1

\int \frac{d}{1} (y) d x

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

(u^{- 2} + u^{- 3}) (u^{5} - 9 u^{2})

What is the derivative of ln(arctan(8x^3)) ?
The derivative of ln(arctan(8x^3)) is (24x^2)/(arctan(8x^3)(64x^6+1))
What is the first derivative of ln(arctan(8x^3)) ?
The first derivative of ln(arctan(8x^3)) is (24x^2)/(arctan(8x^3)(64x^6+1))