What is the derivative of y=(arctan(2x))^2 ?

The derivative of y=(arctan(2x))^2 is (4arctan(2x))/(4x^2+1)

What is the first derivative of y=(arctan(2x))^2 ?

The first derivative of y=(arctan(2x))^2 is (4arctan(2x))/(4x^2+1)

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derivative of

y = (arctan (2 x))^{2}

\frac{4 arctan ( 2 x )}{4 x ^{2} + 1}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (arctan (2 x)) = \frac{2}{4 x ^{2} + 1}

= 2 arctan (2 x) \frac{2}{4 x ^{2} + 1}

Simplify

2 arctan (2 x) \frac{2}{4 x ^{2} + 1} : \frac{4 arctan ( 2 x )}{4 x ^{2} + 1}

= \frac{4 arctan ( 2 x )}{4 x ^{2} + 1}

What is the derivative of y=(arctan(2x))^2 ?
The derivative of y=(arctan(2x))^2 is (4arctan(2x))/(4x^2+1)
What is the first derivative of y=(arctan(2x))^2 ?
The first derivative of y=(arctan(2x))^2 is (4arctan(2x))/(4x^2+1)