Differentiate #sqrt(x-1)/sqrt(x+1)#?

Question

921 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-19T16:31:00

#d/dx (sqrt(x-1)/sqrt(x+1)) = 1/((x+1)sqrt(x-1)sqrt(x+1))#

#d/dx (sqrt(x-1)/sqrt(x+1)) = d/dx ((x-1)^(1/2)(x+1)^(-1/2))#

#d/dx (sqrt(x-1)/sqrt(x+1)) = d/dx ((x-1)^(1/2)) (x+1)^(-1/2)+(x-1)^(1/2)d/dx((x+1)^(-1/2))#

#d/dx (sqrt(x-1)/sqrt(x+1)) = 1/2(x-1)^(-1/2) (x+1)^(-1/2)-1/2(x-1)^(1/2)(x+1)^(-3/2)#

#d/dx (sqrt(x-1)/sqrt(x+1)) = 1/(2sqrt(x-1)sqrt (x+1))-1/2sqrt(x-1)/((x+1)sqrt(x+1))#

#d/dx (sqrt(x-1)/sqrt(x+1)) = 1/2 1/(sqrt(x-1)sqrt(x+1))( 1- (x-1)/(x+1))#

#d/dx (sqrt(x-1)/sqrt(x+1)) = 1/((x+1)sqrt(x-1)sqrt(x+1))#