What is the derivative of (arctan(4x)^2) ?

The derivative of (arctan(4x)^2) is (8arctan(4x))/(16x^2+1)

What is the first derivative of (arctan(4x)^2) ?

The first derivative of (arctan(4x)^2) is (8arctan(4x))/(16x^2+1)

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

\frac{8 arctan ( 4 x )}{16 x ^{2} + 1}

Solution steps

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

Apply the chain rule:

2 arctan (4 x) \frac{d}{d x} (arctan (4 x))

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

\frac{d}{d x} (arctan (4 x)) = \frac{4}{16 x ^{2} + 1}

= 2 arctan (4 x) \frac{4}{16 x ^{2} + 1}

Simplify

2 arctan (4 x) \frac{4}{16 x ^{2} + 1} : \frac{8 arctan ( 4 x )}{16 x ^{2} + 1}

= \frac{8 arctan ( 4 x )}{16 x ^{2} + 1}

What is the derivative of (arctan(4x)^2) ?
The derivative of (arctan(4x)^2) is (8arctan(4x))/(16x^2+1)
What is the first derivative of (arctan(4x)^2) ?
The first derivative of (arctan(4x)^2) is (8arctan(4x))/(16x^2+1)