What is the derivative of arctan(9x) ?

The derivative of arctan(9x) is 9/(81x^2+1)

What is the first derivative of arctan(9x) ?

The first derivative of arctan(9x) is 9/(81x^2+1)

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\frac{d}{d x} (arctan (9 x))

\frac{9}{81 x ^{2} + 1}

Solution steps

\frac{d}{d x} (arctan (9 x))

Apply the chain rule:

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

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

\frac{d}{d x} (9 x) = 9

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

Simplify

\frac{1}{( 9 x ) ^{2} + 1} \cdot 9 : \frac{9}{81 x ^{2} + 1}

= \frac{9}{81 x ^{2} + 1}

What is the derivative of arctan(9x) ?
The derivative of arctan(9x) is 9/(81x^2+1)
What is the first derivative of arctan(9x) ?
The first derivative of arctan(9x) is 9/(81x^2+1)