Question

How do you differentiate `y=csctheta(theta+cottheta)`?

Answer 1

`(dy)/(d theta)=-csctheta(thetacottheta+cot^2theta-1+csc^2theta)`

Explanation:

we will need to use the product rule

`d/(dx)(color(red)(u)color(blue)(v))=color(blue)(v)color(red)((du)/(dx))+color(red)(u)color(blue)((dv)/(dx))`

`y=csctheta(theta+cottheta)`

`(dy)/(d theta)=color(blue)((theta+cottheta))color(red)(d/(d theta)(csctheta))+color(red)(csctheta)color(blue)((dy)/(d theta)(theta+cottheta)`

`(dy)/(d theta)=(theta+cottheta)(-cscthetacottheta)+csctheta(1-csc^2theta)`

tiding up.

`(dy)/(d theta)=-csctheta(thetacottheta+cot^2theta-1+csc^2theta)`