What is the derivative of tan((pix)/2) ?

The derivative of tan((pix)/2) is sec^2((pix)/2) pi/2

What is the first derivative of tan((pix)/2) ?

The first derivative of tan((pix)/2) is sec^2((pix)/2) pi/2

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derivative of

tan (\frac{π x}{2})

sec^{2} (\frac{π x}{2}) \frac{π}{2}

Solution steps

\frac{d}{d x} (tan (\frac{π x}{2}))

Apply the chain rule:

sec^{2} (\frac{π x}{2}) \frac{d}{d x} (\frac{π x}{2})

= sec^{2} (\frac{π x}{2}) \frac{d}{d x} (\frac{π x}{2})

\frac{d}{d x} (\frac{π x}{2}) = \frac{π}{2}

= sec^{2} (\frac{π x}{2}) \frac{π}{2}

What is the derivative of tan((pix)/2) ?
The derivative of tan((pix)/2) is sec^2((pix)/2) pi/2
What is the first derivative of tan((pix)/2) ?
The first derivative of tan((pix)/2) is sec^2((pix)/2) pi/2