How do you differentiate $arctan (\frac{x}{2})$ $arctan(x/2)$ ?

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How do you differentiate $arctan (\frac{x}{2})$ $arctan(x/2)$ ?

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Answer 1 · 2017-10-22T10:39:50

$\frac{2}{x^{2} + 4}$ $2/(x^2+4)$

Explanation:

$arctan (\frac{x}{2}) = {tan}^{- 1} (\frac{x}{2})$ $arctan(x/2)=tan^-1(x/2)$ the derivative of ${tan}^{- 1} (\frac{x}{2}) = \frac{1}{1 + {(\frac{x}{2})}^{2}} = \frac{1}{1 + \frac{x^{2}}{4}} \frac{1}{2} = \frac{1}{2} (\frac{4}{4 + x^{2}}) = \frac{2}{4 + x^{2}}$ $tan^-1(x/2)=1/(1+(x/2)^2)=1/(1+x^2/4)1/2=1/2(4/(4+x^2))=2/(4+x^2$

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How do you differentiate $arctan (\frac{x}{2})$ $arctan(x/2)$ ?

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