`f(x) = (sec(pix))^2` Find the second derivative of the function.

Textbook Question

Chapter 2, 2.4 - Problem 90 - Calculus of a Single Variable (10th Edition, Ron Larson).
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hkj1385 | (Level 1) Assistant Educator

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`f(x) = (sec(pix))^2 = sec^2(pix)`

`f'(x) = 2pisec(pix)*tan(pix)*sec(pix) = 2pisec^2(pix)*tan(pix)`

`f''(x) = 2pi^2*sec^4(pix) + 4pi^2sec^2(pix)*tan^2(pix)`

`or, f''(x) = 2pi^2*sec^2(pix)[sec^2(pix) + 2tan^2(pix)]`

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