# How do you differentiate #f(x)= ( x + 1 )/ ( cot 3x )# using the quotient rule?

##### 1 Answer

Feb 11, 2018

#### Explanation:

#"given "f(x)=(g(x))/(h(x))" then"#

#f'(x)=(h(x)g'(x)-g(x)h'(x))/(h(x))^2larrcolor(blue)"quotient rule"#

#g(x)=x+1rArrg'(x)=1#

#h(x)=cot(3x)rArrh'(x)=-3csc^2(3x)larrcolor(blue)"chain rule"#

#f'(x)=(cot(3x)+3(x+1)csc^2(3x))/(cot^2(3x))#