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Popular >

derivative of 2arctan(8x)

Solution

\frac{d}{d x} (2 arctan (8 x))

Solution

\frac{16}{64 x ^{2} + 1}

Solution steps

\frac{d}{d x} (2 arctan (8 x))

Take the constant out:

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

= 2 \frac{d}{d x} (arctan (8 x))

Apply the chain rule:

\frac{1}{( 8 x ) ^{2} + 1} \frac{d}{d x} (8 x)

= \frac{1}{( 8 x ) ^{2} + 1} \frac{d}{d x} (8 x)

\frac{d}{d x} (8 x) = 8

= 2 \cdot \frac{1}{( 8 x ) ^{2} + 1} \cdot 8

Simplify

2 \cdot \frac{1}{( 8 x ) ^{2} + 1} \cdot 8 : \frac{16}{64 x ^{2} + 1}

= \frac{16}{64 x ^{2} + 1}

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Frequently Asked Questions (FAQ)

What is the derivative of 2arctan(8x) ?
The derivative of 2arctan(8x) is (16)/(64x^2+1)
What is the first derivative of 2arctan(8x) ?
The first derivative of 2arctan(8x) is (16)/(64x^2+1)