How do you differentiate # g(x) =(1+cosx)/(1-cosx) #?
3 Answers
By simplification
Explanation:
Use the quotient rule :
Explanation:
Let
Let
Substituting into the quotient rule:
Explanation:
differentiate using the
#color(blue)"quotient rule"#
#"Given " f(x)=(g(x))/(h(x))" then"#
#f'(x)=(h(x)g'(x)-g(x)h'(x))/(h(x))^2larr" quotient rule"#
#"here " g(x)=1+cosxrArrg'(x)=-sinx#
#h(x)=1-cosxrArrh'(x)=sinx#
#rArrf'(x)=((1-cosx)(-sinx)-(1+cosx)(sinx))/(1-cosx)^2#
#color(white)(rArrf'(x))=(-sinx+sinxcosx-sinx-sinxcosx)/(1-cosx)^2#
#color(white)(rArrf'(x))=-(2sinx)/(1-cosx)^2#