I don't understand implicit differentiation at all. Anyone willing to help?

Question

anonymous · Answer

@peachpi i need ur help

empty · Answer

Yeah I can help you with implicit differentiation, what would you like to know? If you have some problem we could work through or if you want me to make one up it might help.

castiel · Answer

I'm actually studying that too now so I'll try to help as well

loser66 · Answer

Thanks for reply. " I " am offline now. hwahahaha....

anonymous · Answer

@Empty If you could make up a problem and do a step-by-step review that would help a lot. Thank you

empty · Answer

Sure, let's look at this problem and just do implicit differentiation. $$y^{1/2}=x$$ doing implicit differentiation (for no real reason, we could just square both sides and to this normally, but let's pretend we didn't notice  that) we get:

$$\frac{1}{2} y^{-1/2}y' = 1$$

Let's solve for y', 

$$y' = 2y^{1/2}$$

Plug in the original value from the start for $y^{1/2}=x$ to get

$$y'=2x$$ which is totally what we would have gotten had we done it the simpler way.

anonymous · Answer

Okie Doke. Thank you so much @Empty

empty · Answer

That's it? No questions? :?