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

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

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

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

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

\frac{8}{16 x ^{2} + 1}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{8}{16 x ^{2} + 1}

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