It's been a while since I've done derivatives and I'm having problems with these two. I know they aren't horribly complicated, but I just can't seem to get them right

1) Find Y'

2) Find Y''

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- March 31st 2011, 06:30 PMTenaciousEA couple of simple derivative problems
It's been a while since I've done derivatives and I'm having problems with these two. I know they aren't horribly complicated, but I just can't seem to get them right

1) Find Y'

2) Find Y'' - March 31st 2011, 06:34 PMTheChaz
How do you know that you haven't gotten them right? Do you have the solutions? If so, please show your work and many of us would be glad to add our input.

- March 31st 2011, 06:56 PMTenaciousE
Sorry I don't know how to use the text functions to make it look better >.< Anyway, here is what I have so far.

1) y = tan(sqrt(1-x))

y' = .5tan(1-x)^-.5 (sec(1-x))^2

y' = ((sec(1-x))^2)/2tan(1-x)^.5

2) I don't remember much at all about implicit differentiation.. I'm having trouble finding the first derivative

(x^2)(y^3) + 3y^2 = x - 4y

y'((3x^2)(y^2) + 6y + 4) = 1 - 2xy^3

y' = (1 - 2xy^3)/((3x^2)(y^2) + 6y + 4)

I'm not sure if either of these are actually right, but they don't look right. If the second one is right, the second derivative is going to be ridiculous - March 31st 2011, 07:09 PMTheChaz
(Many things clean-up nicely with tex tags. For exponents with more than one character, I used - and you should use! - { } )

I tried to make (1) look ok...

It's wrong, though (if I read your work correctly).

For the sake of my typing, let's call the square root "u".

We have y = tan(u)

Then y' = sec^2(u)*u'

And u' = -.5/u (don't forget to use chain rule TWICE to get the derivative of (1-x)).

2.

I think (trying to format and work it as I go...)! Then divide by the factor next to y'...