Another annoyingly easy question.. (1 Viewer)

[redslert]

arrrrrr my bad bad mistake!
let me fix it!
i made a big mistake!

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

= (x+1)^(1/2) + x / 2(x+1)^(1/2)

Put everything over 2*(x+1)^(1/2) denominator

= [2(x + 1) + x ] / [2*(x+1)^(1/2)]

= [3x + 1] / [2*(x+1)^(1/2)]

= (1/2)*[3x + 1]*[(x+1)^(-1/2)]

looks bad...dunno if it's rite or not...too tired

 

[:: ck ::]

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

= (x+1)^(1/2) + x / 2(x+1)^(-1/2) <-- forgot to do n-1 for power

Put everything over 2*(x+1)^(1/2) denominator

...

mmm if u wish to put it all in one line...

...
= ( x/2 )( x+1 )^(-1/2) + ( x+1 )^1/2
= [ x / ( 2 sqrt ( x+1 ) ] + ( x+1 )^(1/2)
here making 2 sqrt (x+1) common denominator :
= x + 2 * (x+1)^(1/2) * (x+1)^(1/2)
---------------------------------------------
2(x+1)^(1/2)

= [ x + 2(x+1) ] / (2x+1)^(1/2)

putting it in one line :

= ( 3x+2 ) ( 2sqrt ( x+1 ) )^(-1)