Question

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

Answer 1

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)`