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. $u=sqrt(x-1)$

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

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

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

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