Find and simplify y prime when y=arcsin(2x-1)

Question

hartnn · Answer

do u know the derivative of arcsin t ?

anonymous · Answer

would it be arccos?

hartnn · Answer

no.

hartnn · Answer

derivative of arcsin t is 1/sqrt(1-t^2)
ok?

anonymous · Answer

oh okay, so I would just plug the 2x-1 into t and then find the derivative of 2x-1 and simplify?

hartnn · Answer

exactly! yes, use of chain rule..

anonymous · Answer

ahh, thank you.

hartnn · Answer

so what u got finally ?

hartnn · Answer

just to verify u did it correctly....

anonymous · Answer

1/squareroot(x-x^2)

hartnn · Answer

good work :) thats correct!

anonymous · Answer

thanks can you help me with another problem: If coshx=4/3 and 0 is less than x, find the value of sinhx? What is the first step I would take?

hartnn · Answer

know the formula relating sinh x and cosh x ??

anonymous · Answer

No I do not

hartnn · Answer

then how come you are attempting this question ?

hartnn · Answer

$\huge \color{red}{\cosh^2x-\sinh^2x=1}$

anonymous · Answer

I mean I know that the derivative of cosh is sinh and vise versa, but as far as a formula to solve it, my teacher did not provide that. Just trying to understand the last bit of review before a final tomorrow. Thanks for the formula.

hartnn · Answer

now will u be able to get sinh x ?

anonymous · Answer

yes, thank you. sorry for the trouble

hartnn · Answer

no problem at all...
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