Question

How do you find the derivative of `y = csc^3(2x)`?

Answer 1

`dy/dx=-6csc^3(2x)cot(2x)`

Explanation:

`"differentiate using the "color(blue)"chain rule"`

`"given "y=f(g(x))" then"`

`dy/dx=f'(g(x))xxg'(x)larrcolor(blue)"chain rule"`

`y=csc^3(2x)=(csc(2x))^3`

`dy/dx=3(csc(2x))^2xxd/dx(csc(2x))`

`color(white)(dy/dx)=3csc^2(2x)xx-csc(2x)cot(2x)xxd/dx(2x)`

`color(white)(dy/dx)=-6csc^3(2x)cot(2x)`