What is the derivative of $tan (\frac{π \cdot x}{2})$ $tan((pi * x)/2)$ ?

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What is the derivative of $tan (\frac{π \cdot x}{2})$ $tan((pi * x)/2)$ ?

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Answer 1 · 2016-07-03T16:15:21

Derivative of $tan (\frac{π \cdot x}{2})$ $tan((pi*x)/2)$ is $\frac{π}{2} {sec}^{2} (\frac{π \cdot x}{2})$ $pi/2sec^2((pi*x)/2)$

Explanation:

$f (x) = tan (\frac{π \cdot x}{2})$ $f(x)=tan((pi*x)/2)$

Hence $\frac{d f}{d x} = \frac{d}{d (\frac{π \cdot x}{2})} tan (\frac{π \cdot x}{2}) \times \frac{d}{d x} (\frac{π \cdot x}{2})$ $(df)/(dx)=d/(d((pi*x)/2))tan((pi*x)/2)xxd/(dx)((pi*x)/2)$

= ${sec}^{2} (\frac{π \cdot x}{2}) \times \frac{π}{2}$ $sec^2((pi*x)/2)xxpi/2$

= $\frac{π}{2} {sec}^{2} (\frac{π \cdot x}{2})$ $pi/2sec^2((pi*x)/2)$

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What is the derivative of $tan (\frac{π \cdot x}{2})$ $tan((pi * x)/2)$ ?

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Explanation:

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