How do you differentiate #f(x)= (1 - sin^2x)/cosx # using the quotient rule?

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Answer 1 · 2018-04-30T13:00:39

the answer #f'(x)=-sinx#

The common way is

#sin^2(x)+cos^2(x)=1#

#cos^2(x)=1-sin^2(x)#

#f(x)= (1 - sin^2x)/cosx=cos^2(x)/cos(x)=cos(x)#

#f'(x)=-sin(x)#

#y=f(x)/g(x)#

#y'=[g(x)*f'(x)-f(x)*g'(x)]/(g(x))^2#

#f(x)= (1 - sin^2x)/cosx#

#f'(x)=(sin(x)*(1-sin(x)^2)-2*cos(x)^2*sin(x))/cos(x)^2#

#=((sin(x)*(1-sin(x)^2))/cos(x)^2)-2*sin(x)#

= #(sin(x)*cos^2(x))/cos^2(x)-2sinx#

= #sinx-2sinx#

= #-sinx#