How do you differentiate #(x^3-x+3 )/ (cos^2x)# using the quotient rule?
1 Answer
Jul 4, 2017
Explanation:
#"given " f(x)=(g(x))/(h(x))" then"#
#f'(x)=(h(x)g'(x)-g(x)h'(x))/(h(x))^2#
#g(x)=x^3-x+3rArrg'(x)=3x^2-1#
#h(x)=cos^2x=(cosx)^2#
#rArrh'(x)=2cosx(-sinx)larr" chain rule"#
#rArrf'(x)=(cos^2x(3x^2-1)-(x^3-x+3)(-2sinxcosx))/(cos^2x)^2#
#=((3x^2-1)cos^2x+sin2x(x^3-x+3))/(cos^4x)#
