What is the derivative of $arctan (\frac{x}{2})$ $arctan (x/2)$ ?

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Answer 1 · 2016-06-26T07:29:17

$\frac{d y}{d x} = \frac{1}{2} {cos}^{2} (arctan (\frac{x}{2}))$ $(dy)/(dx)=1/2cos^2(arctan(x/2))$

As $y = arctan (\frac{x}{2})$ $y=arctan(x/2)$

$tan y = \frac{x}{2}$ $tany=x/2$

Hence, ${sec}^{2} y \times \frac{d y}{d x} = \frac{1}{2}$ $sec^2yxx(dy)/(dx)=1/2$ or

$\frac{d y}{d x} = \frac{1}{2} {cos}^{2} y = \frac{1}{2} {cos}^{2} (arctan (\frac{x}{2}))$ $(dy)/(dx)=1/2cos^2y=1/2cos^2(arctan(x/2))$

What is the derivative of arctan (x/2)arctan(x2)arctan (x/2)?