What is the derivative of $y = sec (x) tan (x)$ $y=sec(x) tan(x)$ ?

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Answer 1 · 2014-09-11T21:28:22

By Product Rule, we can find
$y' = sec x (1 + 2 {tan}^{2} x)$ $y'=secx(1+2tan^2x)$ .

Let us look at some details.
$y=secxtanx$

By Product Rule,
$y'=secxtanx cdot tanx+secx cdot sec^2x$

by factoring out $sec x$ ,
$=secx(tan^2x+sec^2x)$

by $sec^2x=1+tan^2x$ ,
$=secx(1+2tan^2x)$

What is the derivative of y=sec(x) tan(x)y=sec(x)tan(x)y=sec(x) tan(x)?