What is the derivative of ${sec}^{2} π (x)$ $Sec^2 pi(x)$ ?

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Answer 1 · 2017-06-07T15:05:30

$\frac{d y}{d x} = 2 π {sec}^{2} π x tan π x$ $dy/dx = 2pisec^2pixtanpix$

Use the chain rule to differentiate $y = {sec}^{2} π x$ $y=sec^2pix$

Let $u = sec π x$ $u=secpix$ and $y = u^{2}$ $y=u^2$

$\frac{d y}{d u} = 2 u = 2 sec π x$ $dy/(du) = 2u=2secpix$

$\frac{d u}{d x} = π sec π x tan π x$ $(du)/dx= pisecpixtanpix$

Chain rule:

$\frac{d y}{d x} = \frac{d y}{d u} \times \frac{d u}{d x}$ $dy/dx=dy/(du) xx (du)/dx$

$\frac{d y}{d x} = 2 sec π x \times π sec π x tan π x = 2 π {sec}^{2} π x tan π x$ $dy/dx = 2secpix xx pisecpixtanpix = 2pisec^2pixtanpix$

What is the derivative of Sec^2 pi(x) sec2π(x)Sec^2 pi(x) ?