How do you find the derivative of #1/sqrt (x-1)#?

2 Answers
Aug 1, 2017

Answer:

The derivative is #=-1/(2(x-1)^(3/2))#

Explanation:

We need

#(x^n)'=nx^(n-1)#

Our function is #f(x)=1/sqrt(x-1)=(x-1)^(-1/2)#

#AA x in (1, +oo)#, #f(x) in (0,+oo)#

#f'(x)=((x-1)^(-1/2))'=-1/2*(x-1)^(-3/2)=-1/(2(x-1)^(3/2))#

Aug 1, 2017

Answer:

#-1/(2sqrt((x-1)^3))#

Explanation:

#"express "y=1/(sqrt(x-1))=(x-1)^(-1/2)#

#"differentiate using the "color(blue)"chain rule"#

#"given "y=f(g(x))" then"#

#dy/dx=f'(g(x)xxg'(x)larr" chain rule"#

#y=(x-1)^(-1/2)#

#rArrdy/dx=-1/2(x-1)^(-3/2)xxd/dx(x-1)#

#color(white)(rArrdy/dx)=-1/(2sqrt((x-1)^3))#