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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\frac{d}{d x} (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}

y = (9 x)^{3 x}

\int \frac{1}{x ( x - 5 ) ^{2}} d x

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

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

\int (2 x - 1) (3 x + 4) d x

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)