How do you find the derivative of #tanx/sinx#?

1 Answer
Jul 15, 2016

#d/dx[tan x/sinx] = d/dx[sec x] = sec x tan x#

Explanation:

Before we try to take a derivative, we could still simplify this expression.

Since #tan x = (sinx)/(cosx)#, we can write

#tanx/(sinx) = (cancel(sinx)/cosx * 1/(cancel(sinx)))/cancel((sinx/1 * 1/sinx)) = 1/cosx = sec x#

Also, we know by definition that #d/dx[sec x] = secx tanx#, thus giving us

#d/dx[tan x/sinx] = d/dx[sec x] = sec x tan x#