need some help with derivative problems

[slinky2004]

i'm trying to work these two deriviative problems for my homework, but i'm not sure i'm doing these right.

one is a chain/product rule derivative:
1. y=1/2x^2 * (16x-x^2)^1/2
i set up:
y'=x(16x-x^2)+1/2(16x-x^2)^-1/2(-2x)(1/2x^2)
and after i work it out and simplify i get:
y'=x(16-x^2)^1/2(-8x^3+1/2x^5)^1/2+1
(-8x^3+1/2x^5)^1/2
is that even close?

the other is a multple chain rule with trig functions(the PI is pi and the t is just a variable:
2. y=5cos^2(PI*t)
so i did:
y=5(cos(PI*t)^2
y'=10(cos(PI*t))*[-sin(PI*t)*PI]
y'=-10PIsin(PI*t)cos(PI*t)

i think i can go farther with it, but i dont know what to do next.

 

[stapel]

When using the Chain Rule, you know you're "done" when you've gotten down to the variable. So, for (2), you got down to differentiating "(pi)t", which is the variable (times a constant), and you're done. Good job!

For (1), though, I'm a little fuzzy. I think you mean the following:

. . . . .y = (1/2) x² (16x - x²)

...but your answer contains fractions (that's what the underline is for...?), so I think I must be mistaken...?

Please reply, using grouping symbols for clarification. Thank you!

Eliz.

 

[slinky2004]

yeah, it was supposed to be to the 1/2 power in the original problem, i'll fix it.

 

[stapel]

Is everything raised to the one-half power, or just the contents of the last parentheses?

Is the first bit "one over 2x²", or "one-half times x²"?

Thank you.

Eliz.

 

[slinky2004]

just the second part, like this:
y=1/2x^2 * (16x-x^2)^1/2