What is the derivative of tan(pi/2 x) ?

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

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

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

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\frac{d}{d x} (tan (\frac{π}{2} x))

sec^{2} (\frac{π x}{2}) \frac{π}{2}

Solution steps

\frac{d}{d x} (tan (\frac{π}{2} x))

Simplify

tan (\frac{π}{2} x) : tan (\frac{π x}{2})

= \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}

\int sec^{3} (x) tan^{3} (x) d x

y^{^{'}} + (1 - \frac{1}{x}) y = x^{2}

\frac{3}{x - 2}

\int \frac{x ^{2}}{( x ^{2} + 9 ) ^{3}} d x

x \to 4 lim (x)

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