Question 1190800
Differentiate

a)

{{{(2-sqrt(x))^6}}}  

{{{(d/dx)((2 - sqrt(x))^6)}}} ..........apply the chain rule

={{{6(2 -sqrt(x))^5(d/dx)(2-sqrt(x))}}}........{{{(d/dx)(2 - sqrt(x))=-1/(2sqrt(x))}}}

={{{6(2 - sqrt(x))^5*(-1/(2sqrt(x)))}}}........simplify

={{{-3(2 - sqrt(x))^4*(1/sqrt(x))}}}

={{{ -(3 (2 - sqrt(x))^5)/sqrt(x)}}}



b) 

{{{1/(1-1/x)^3}}}


{{{ (d/dx) (1/(1-1/x)^3)}}}........... apply exponent rule: {{{1/a=a^-1}}}

={{{(d/dx) ((1-1/x)^-3)}}} .........apply the chain rule

={{{-3/((1-1/x)^4)(d/dx)(1-1/x)}}}.........{{{(d/dx)(1-1/x)=1/x^2}}}

={{{-3/(((x-1)/x)^4)(1/x^2)}}}......simplify

={{{-3/((x-1)^4/x^4)(1/x^2)}}}

={{{-3/((x-1)^4/x^4)(1/x^2)}}}

={{{-3x^4/((x-1)^4)(1/x^2)}}}.....simplify

={{{-3x^2/((x-1)^4)}}}



c)

assuming you have

{{{1/(2(3x-2)^2)}}}

{{{ (d/dx)(1/(2(3x-2)^2))}}}...........take the constant out 
 
={{{(1/2)(d/dx)(1/(3x-2)^2)}}}....... apply exponent rule

={{{(1/2)(d/dx)((3x-2)^-2)}}}.........apply the chain rule

={{{(1/2)(-2/((3x-2)^3))(d/dx)(3x-2)}}}..........{{{(d/dx)(3x-2)=3}}}

={{{(2/(-2(3x-2)^3))(3)}}}......simplify

={{{(-1/((3x-2)^3))(3)}}}

={{{-3/(3x-2)^3}}}