`y = ((sec(x))^7)/7 - ((sec(x))^5)/5` Find the derivative of the function.

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Chapter 2, Review - Problem 60 - Calculus of a Single Variable (10th Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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Given: `y=(sec(x))^7/7-(sec(x))^5/5`

`y'=(7sec(x)^6)/7sec(x)tan(x)-(5sec(x)^4)/5sec(x)tan(x)`

`y'=(sec(x))^7tan(x)-(sec(x))^5tan(x)`

`y'=(sec(x))^5tan(x)[(sec(x))^2-1]`

`y'=(sec(x))^5tan(x)(tan(x))^2`

`y'=(sec(x))^5(tan(x))^3`

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