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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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