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Popular >

derivative of (arctan(9x))^2

Solution

derivative of

(arctan (9 x))^{2}

Solution

\frac{18 arctan ( 9 x )}{81 x ^{2} + 1}

Solution steps

\frac{d}{d x} ((arctan (9 x))^{2})

Apply the chain rule:

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

= 2 arctan (9 x) \frac{d}{d x} (arctan (9 x))

\frac{d}{d x} (arctan (9 x)) = \frac{9}{81 x ^{2} + 1}

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

Simplify

2 arctan (9 x) \frac{9}{81 x ^{2} + 1} : \frac{18 arctan ( 9 x )}{81 x ^{2} + 1}

= \frac{18 arctan ( 9 x )}{81 x ^{2} + 1}

Graph

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x \to 0 lim (cos (x) + sin (x))

Frequently Asked Questions (FAQ)

What is the derivative of (arctan(9x))^2 ?
The derivative of (arctan(9x))^2 is (18arctan(9x))/(81x^2+1)
What is the first derivative of (arctan(9x))^2 ?
The first derivative of (arctan(9x))^2 is (18arctan(9x))/(81x^2+1)