What is the (arctan(3x))^' ?

The (arctan(3x))^' is 3/(9x^2+1)

What is the first (arctan(3x))^' ?

The first (arctan(3x))^' is 3/(9x^2+1)

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(arctan (3 x))^{^{'}}

\frac{3}{9 x ^{2} + 1}

Solution steps

(arctan (3 x))^{'}

Apply the chain rule:

\frac{1}{( 3 x ) ^{2} + 1} (3 x)^{'}

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

(3 x)^{'} = 3

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

Simplify

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

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

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