How do you differentiate #f(x)=csc^2(3x ) # using the chain rule?

1 Answer
Feb 11, 2018

Answer:

#f'(x)=-6csc^2(3x)cot(3x)#

Explanation:

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

#f'(x)=g'(h(x))xxh'(x)larrcolor(blue)"chain rule"#

#f(x)=csc^2(3x)=(csc(3x))^2#

#f'(x)=2csc(3x)xxd/dx(csc(3x))xxd/dx(3x)#

#color(white)(f'(x))=2csc(3x)xx-csc(3x)cot(3x)xx3#

#color(white)(f'(x))=-6csc^2(3x)cot(3x)#