Please Help Me with This Chain Rule Problem Before I lose it!!!

Find the derivative of y= x sqrtx-7

Answer = 3x-14/2sqrtx-. WHY??? Please help I have an exam in 2 days im freaking out!!!!

I got this far: rewrote as x(x-7)1/2 So this turns to 1/2x(x-7)^-1/2
then the derivative of inside bracket is 1. What the hell I dont understand where 3x - 14 comes from at all.

PLEASE PLEASE HELP

You have to use product rule:

Y= x* sqr(x-7)

Y= x* (x-7)^(1/2)

***edit : the product rule : d(u*v)= u*dv + v*du or (first factor * deriv. Of second ) + ( second factor * deriv of first)

So the first factor is x. Its deriv is 1

The second factor is ( x-7)^(1/2). its deriv by power/ chain rule is
(1/2) (x-7)^ (-1/2)* 1

Y'= x[(1/2)(x-7)^(-1/2)](1) + (x-7)^(1/2) *1

You have two big terms, so try to factor.
Factor out (1/2) (x-7)^(-1/2) because it has the smallest power, and the fraction coefficient:

Y'= (1/2)(x-7)^(-1/2)* [ x+2(x-7)]
*** ***
Do you see how the factoring worked? Both terms have (x-7), so take out the smallest power.

Like u^-1/2 + u^(1/2)= u^(-1/2)[ 1+ u]
*******

Simplify the [x+2(x-7)] = x+2x-14= 3x-14
Then the 1/2 and the neg. Exponent go to the denom. As 2(x-7)^(1/2)
********
= (3x-14)/[2(x-7)^(1/2)]

Hoping this helps!

don't know about your algebra or differentiation techniques

y = x √ ( x - 7 ) ---> dy / dx = √(x - 7 ) + x / [ 2 √ ( x- 7 ) ]

and after algebra dy / dx = { 2 ( x - 7 ) + x } / [ 2 √ ( x - 7 ) ] = [ 3x - 14 ] / [ 2 √ ( x- 7 ) ]

common denominators...