Quick Calculus question

[MangoTBG]

Ok, maybe I'm just really tired from studying but this is an oldie but goodie

What is, or rather how do I do? , the derivative of f(x)=sin(x)cos(x) ?

That's sin(x) multiplied by cos(x).

Or better yet, if anyone can help me find a list of these trig functions and their derivatives that'd be helpful. It's hard (atleast for me) to effectively google for these type of notations.

Below is my earlier question quoted for those that weren't around for it...

This might even be trigonometry?

What shape is X^2 + Y^2 = 2Y?

Really, I guess the question is is this a circle?

I know X^2 + Y^2 = 3X is a circle, but does it make a difference that the RHS has a Y variable rather than a X variable?

 

[chuckywang]

Yes, it's a circle.

 

[MangoTBG]

That's what I thought.

When I turned it into a polar equation I got r=2 sin (theta) which when graphed is a circle. But when looking at the cartesian coordinates it the varible on the RHS was throwing me off.

Thanks.

 

[chuckywang]

Rewrite the equation as: x^2 + (y-1)^2 = 1.

That is a circle of radius 1 centered at (0,1).

 

[msparish]

You can move the 2Y to the left side, and then complete the square to get the standard equation of a circle.

 

[MangoTBG]

Thank you ATOTutors!

 

[MangoTBG]

Bump, can an ATOT brother help another out? 🙂

 

[interchange]

d/dx[f(x)g(x)] = f(x)g'(x) + g(x)f'(x)

capiche?

 

[BrownTown]

On a related note the integral is also pretty easy using integration by parts.

 

[MangoTBG]

Yes, that f#$*ing makes perfect sense!


Curious why I'm so aweful at this right now? Probably not, but if you are reading this...then hell maybe you are?

I took AP BC Calculus (Calc I and II) in highschool. That was Fall 2002/Spring 2003...I'm just now taking Calculus III. A lot of this stuff is coming back to me, but I'm forgeting some key things. Like I just had to go over the chain rule, but I totally got it within 5 minutes of looking at it again.

I do remember, now, that it's the orginal function of one multiplied by the derivative of the other + vice versa. Thanks!

How much do I owe you guys?