What is the derivative of arctan(8x) ?

The derivative of arctan(8x) is 8/(64x^2+1)

What is the first derivative of arctan(8x) ?

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

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derivative of

arctan (8 x)

\frac{8}{64 x ^{2} + 1}

Solution steps

\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

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

Simplify

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

= \frac{8}{64 x ^{2} + 1}

\frac{d}{d x} (2 x^{5} - 6 x^{4} + 4 x^{3} + 4 x^{2} - 6 x + 2)

\int (x - 2) d x

\frac{d}{d x} (\frac{3 ( - x ^{2} + 1 )}{( x ^{2} + 1 ) ^{2}})

y^{^{''}} + 2 y^{^{'}} + y = - 2 e^{x}

\frac{d y}{d x} = \frac{x - 4}{y - 6}

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