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

The derivative of ln(arctan(3x^3)) is (9x^2)/(arctan(3x^3)(9x^6+1))

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

The first derivative of ln(arctan(3x^3)) is (9x^2)/(arctan(3x^3)(9x^6+1))

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

\frac{9 x ^{2}}{arctan ( 3 x ^{3} ) ( 9 x ^{6} + 1 )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (arctan (3 x^{3})) = \frac{9 x ^{2}}{9 x ^{6} + 1}

= \frac{1}{arctan ( 3 x ^{3} )} \cdot \frac{9 x ^{2}}{9 x ^{6} + 1}

Simplify

\frac{1}{arctan ( 3 x ^{3} )} \cdot \frac{9 x ^{2}}{9 x ^{6} + 1} : \frac{9 x ^{2}}{arctan ( 3 x ^{3} ) ( 9 x ^{6} + 1 )}

= \frac{9 x ^{2}}{arctan ( 3 x ^{3} ) ( 9 x ^{6} + 1 )}

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

(1 + cos (t)) y^{^{'}} = (1 + e^{- y}) sin (t)

\frac{d}{d x} (lo g_{4} (2 x + 3))

f (x) = (5 t^{2} - 2 t + 1)^{\frac{3}{2}}

What is the derivative of ln(arctan(3x^3)) ?
The derivative of ln(arctan(3x^3)) is (9x^2)/(arctan(3x^3)(9x^6+1))
What is the first derivative of ln(arctan(3x^3)) ?
The first derivative of ln(arctan(3x^3)) is (9x^2)/(arctan(3x^3)(9x^6+1))