What is the derivative of $arctan (\frac{x}{3})$ $arctan(x/3)$ ?

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Answer 1 · 2015-06-15T19:38:07

$\frac{d}{d x} [arctan u] = \frac{1}{1 + u^{2}} (\frac{d u}{d x})$ $d/(dx)[arctanu] = 1/(1+u^2)((du)/(dx))$

$\Rightarrow \frac{1}{1 + \frac{x^{2}}{9}} \cdot \frac{1}{3} = \frac{1}{3 + \frac{x^{2}}{3}}$ $=> 1/(1+x^2/9)*1/3 = 1/(3+x^2/3)$

$= \frac{3}{9 + x^{2}}$ $= 3/(9+x^2)$

What is the derivative of arctan(x3)arctan(x/3)?