What is the derivative of arctan(3x) ?

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

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

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

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derivative of

arctan (3 x)

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

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d 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}

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