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