How do you find the derivative of (1-secx)/tanx?

1 Answer
May 15, 2015

We could use the quotient rule and differentiate the function from this form, but it may be simpler to rewrite the function first:

f(x)=(1-secx)/tanx = 1/tanx -secx/tanx

color(white)"ssss" = cotx -secxcotx

color(white)"ssss" = cotx - cscx

Now it is a matter on knowing these derivatives (memorize them):

f'(x)=-csc^2x-(-cscxcotx)=cscxcotx-csc^2x

Or, if you prefer:

f'(x) = cscx(cotx-cscx)