What is the derivative of this function #y=cot^-1(sqrt(x-1))#?

1 Answer
Aug 9, 2018

#(dy)/(dx)=-1/(2xsqrt(x-1))#

Explanation:

Here ,

#y=cot^-1(sqrt(x-1))#

Let ,

#y=cot^-1u and u=sqrt(x-1)#

#:.(dy)/(du)=-1/(1+u^2) and (du)/(dx)=1/(2sqrt(x-1)#

Using Chain Rule:

#color(blue)((dy)/(dx)=(dy)/(du)(du)/(dx)#

#:.(dy)/(dx)=(-1)/(1+u^2)*1/(2sqrt(x-1))#

Subst. #u=sqrt(x-1)#

#:.(dy)/(dx)=-1/(1+(sqrt(x-1))^2) xx1/(2sqrt(x-1))#

#:.(dy)/(dx)=-1/(1+x-1)xx1/(2sqrt(x-1))#

#:.(dy)/(dx)=-1/(2xsqrt(x-1))#