inverse trig derivative questions!

[ihatecalc]

i get the basic problems, but i dont know how to do the more complicated ones!

such as,

1.) y = arcsin (1/t), 0<t<1

and

2.) y = s(sqrt(s-s^2)) + arccos (s)

if i get these two problems, i may be able to figure out how to do the rest of my homework. PLEASE help me!!! im desperate.

 

[skeeter]

for \(\displaystyle \L y = \arcsin{(\frac{1}{t})}\) ...

\(\displaystyle \L \frac{d}{dt}[\arcsin{(u)}] = \frac{1}{\sqrt{1 - u^2}} \cdot \frac{du}{dt}\)

your "u" is 1/t ... du/dt = -1/t², correct?

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for \(\displaystyle \L y = s \sqrt{s - s^2} + \arccos(s)\) ...

use the product and chain rule for the term \(\displaystyle \L s \sqrt{s - s^2}\)

for the 2nd term ...
\(\displaystyle \L \frac{d}{ds}[\arccos{(s)}] = \frac{-1}{\sqrt{1 - s^2}}\)