Prove that `d/(dx) (sec(x)) = sec(x) tan(x)`

Textbook Question

Chapter 3, 3.3 - Problem 18 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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kspcr111 | In Training Educator

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`d/(dx) (sec(x))`

`=d/(dx) (1/cos(x))`

`= ((d/(dx) cos x)*1 - cosx * d/dx(1))/(cos^2(x))`

`= sinx/cos^2(x)`

`= sec(x) tan(x)`

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