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

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Answer 1 · 2018-08-09T19:17:59

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

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)#

#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))#