derivative of tan((pix/2)) — step-by-step solution

⚠ pix is read as the product π*x

Let's perform the differentiation:

\frac{d}{d x} (\tan (π \cdot \frac{x}{2}))

Apply the differentiation rule:

\frac{d}{d x} (\tan (f)) = \frac{d}{d x} (f) \cdot \frac{1}{{\cos (f)}^{2}}

with f =

\frac{π x}{2}

\frac{d}{d x} (\frac{π x}{2}) \cdot \frac{1}{{\cos (\frac{π x}{2})}^{2}}

\frac{\frac{π}{2}}{{\cos (\frac{π x}{2})}^{2}}

\frac{π}{2} \cdot \frac{1}{{\cos (\frac{π x}{2})}^{2}}

▶Derivative:

\frac{π}{2 \cdot {\cos (\frac{π x}{2})}^{2}}