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

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Answer 1 · 2015-05-15T13:58:24

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)#