What is the derivative of $y = \frac{sec x}{tan x}$ $y = secx/tanx$ ?

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Answer 1 · 2016-10-28T14:54:32

$y' = -cotxcscx$

Let's rewrite the function $y = secx/tanx$ in sine and cosine.

$y = secx/tanx$

Apply the identities $sectheta = 1/costheta$ and $tantheta = sintheta/costheta$ .

$y = (1/cosx)/(sinx/cosx)$

$y = 1/cosx xx cosx/sinx$

$y = 1/sinx$

We can now use the quotient rule to differentiate.

$y' = (0 xx sinx - cosx xx 1)/(sinx)^2$

$y' = -cosx/sin^2x$

$y' = -cosx/sinx xx 1/sinx$

Apply the identities $cosx/sinx = cotx$ and $1/sinx = cscx$ .

$y' = -cotxcscx$

Hopefully this helps!

What is the derivative of y = secx/tanxy=secxtanxy = secx/tanx?