Question

Diffrentiate cot–¹(cosecx-cotx) w.r.t x

Answer 1

thus by using chain rule we will differentiate this

Answer 2

let,
y= cot–¹(cosecx-cotx)
differentiate both sides with respect to x ,

dy/dx = d{cot–¹(cosecx-cotx)}/dx
Using chain rule,
dy/dx =[1/{1 +(cosecx-cotx)²}] d(cosecx-cotx)/dx
dy/dx = [1/{1 +(cosecx-cotx)²}] (-cosecx.cotx- cosec²)
Now simplying the following we get ,
(See picture)
dy/dx= 1/2{(1+cosx)/(1-cosx)}



We know that ,
d(cot-¹)/dx = -1/(1+x²)
d(cosec x)/dx = -cosecx*cotx
d(cotx)/dx= -cosec²x