Question

Question #c9eb0

Answer 1

`6xcsc^2(3x^2)`

Explanation:

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(cotx)=-csc^2x)color(white)(2/2)|)))`

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

`color(red)(bar(ul(|color(white)(2/2)color(black)(dy/dx=(dy)/(du)xx(du)/(dx))color(white)(2/2)|)))`

`"let " u=3x^2rArr(du)/(dx)=6x`

`rArry=-coturArr(dy)/(du)=-(-csc^2u)=csc^2u`

Complete the derivative, changing u back into terms of x

`rArrd/dx(-cot(3x^2))=csc^2uxx6x=6xcsc^2(3x^2)`