What is the derivative of arctan(x/6) ?

The derivative of arctan(x/6) is 6/(x^2+36)

What is the first derivative of arctan(x/6) ?

The first derivative of arctan(x/6) is 6/(x^2+36)

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\frac{d}{d x} (arctan (\frac{x}{6}))

\frac{6}{x ^{2} + 36}

Solution steps

\frac{d}{d x} (arctan (\frac{x}{6}))

Apply the chain rule:

\frac{1}{( \frac{x}{6} ) ^{2} + 1} \frac{d}{d x} (\frac{x}{6})

= \frac{1}{( \frac{x}{6} ) ^{2} + 1} \frac{d}{d x} (\frac{x}{6})

\frac{d}{d x} (\frac{x}{6}) = \frac{1}{6}

= \frac{1}{( \frac{x}{6} ) ^{2} + 1} \cdot \frac{1}{6}

Simplify

\frac{1}{( \frac{x}{6} ) ^{2} + 1} \cdot \frac{1}{6} : \frac{6}{x ^{2} + 36}

= \frac{6}{x ^{2} + 36}

\int x ln (8 x) d x

y^{'} = 0.0016 y (2500 - y)

y^{^{'}} - y = 6 t e^{2 t}

f (x) = 1 - 4 x, at x = - 1

(x + x) \frac{d y}{d x} = y + y

What is the derivative of arctan(x/6) ?
The derivative of arctan(x/6) is 6/(x^2+36)
What is the first derivative of arctan(x/6) ?
The first derivative of arctan(x/6) is 6/(x^2+36)