1. Chain Rule

Reviewing the chain rule.

1. 8sqrt(x^4-4x^2)

I don't know if I'm simplifying it wrong, but I'm not getting the correct answer.

2. csc^2x^2

I don't know why these always give me a hard time. =/

Any help would be greatly appreciated.

Thanks!

2. 1. 8sqrt(x^4-4x^2)

MATH]8*(x^4-4x^2)^(1/2)[[/tex]....exponentially sqrt=x^(1/2)

Outer function is y= 8u^(1/2)
Inner function is u=x^4- 4x^2
rememberthe chain rule is dy/dx= dy/du * du/dx

Derivativeof y= 8u^(1/2) ..... power rule

$8*.5u^(1/2-1)$

$\frac{1}{8sqrt (u)}$

Now,
$\frac{1}{8sqrt (x^4- 4x^2)}$ * $4x^3 - 8x$

Then simplify,
$\frac{4x^3 - 8x}{8sqrt (x^4- 4x^2)}$

2. Use parenthesis to say what the equation is.
Is it (csc^2x)^2 or perhaps (csc)^2x^2 ?

3. The answer is (16x^2-32)/(sqrt (x^2-4)).

I got (16x^2-32)/(sqrt (x^4-4x^2)).

I have no idea where their answer came from.

The second is written as (csc)^2(x^2)