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Popular >

derivative of y=(arctan(9x))^2

Solution

derivative of

y = (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}

Popular Examples

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\int 3 y^{3} d y

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\frac{d}{d x} ((f (x) (5 x))^{2} - 2)

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x \to 4 lim (\frac{7 x + 6}{3 x - 2})

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\int \frac{x ^{2} - 5 x + 16}{( 2 x + 1 ) ( x - 2 ) ^{2}} d x

Frequently Asked Questions (FAQ)

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