Mastering Derivatives: How to Solve a Complex Chain Rule Problem

[soccerboy2209]

Need Help with a Derivative!

Homework Statement

{6x+[8x^(1/2)]}^(1/2)

Homework Equations

I know its chain rule with a square root inside a square root but i can not seem to get the right answer to enter into the computer program my college uses

The Attempt at a Solution

 

[Bohrok]

So you want help to rewrite it in a way that will work in the program?
Try entering it with just parentheses ().

 

[soccerboy2209]

No i can not seem to get the solution

 

[soccerboy2209]

The square root inside a square root is throwing me off

 

[Bohrok]

Is this what it looks like?

$$\sqrt{6x + 8\sqrt{x}}$$

 

[soccerboy2209]

no the 8 is also inside the inner square root

 

[Bohrok]

You didn't use parentheses correctly, then. 8x needs to be in parentheses.

{6x+[(8x)^(1/2)]}^(1/2)

 

[soccerboy2209]

Ok but that is the problem and i need the solution

 

[Bohrok]

How are you entering it into the program?

 

[soccerboy2209]

(1/2){[6+(8x)^(1/2)]^(-1/2)}{6+(4x)^(-1/2)]

 

[Bohrok]

Have you tried with just parentheses () and no square brackets [] or curly braces {} ?

 

[soccerboy2209]

yes but this provides me with the answer i have worked out which is (1/2){6+(8x)^(1/2)]^(-1/2)}[6+(1/2)(8x)^(-1/2)](1/2)[(8x)^(-1/2)](8) and the hint says "You start
with (6x+(8x)^.5))^.5. The inside is (6x+(8x)^.5). So, use the chain
rule on that. Once you have that and have to take the derivative of the
inside, then you need to also do the chain rule with the inside of 8x."

 

[Bohrok]

So you're having trouble doing it by hand on paper?

 

[soccerboy2209]

i guess..if my answer doesn't look right, but i believe i am getting the right answer