`y = sec^2(m theta)` Find the derivative of the function.

Textbook Question

Chapter 3, 3.4 - Problem 32 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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hkj1385 | (Level 1) Assistant Educator

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Note:- 1) If y = secx ; then dy/dx = sex*tanx

2) If y = x^n ; then dy/dx = n*{x^(n-1)} ; where n = real number

3)If y = a*x ; then dy/dx = a ; where a = constant

Now, 

Let theta be represented as 'x' ; then

y = sec^2(mx)

dy/dx = y' = [2*sec(mx)]*[sec(mx)*tan(mx)]*[m]

or, dy/dx = 2*m*tan(mx)*[sec^2(mx)]

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