Chain rule!

f(x) = sin (sqrt[x]) + sqrt[sin x]

Question

Chain rule!

f(x) = sin (sqrt[x]) + sqrt[sin x]

anonymous · Answer

f(x) = $$\sin \sqrt{x}$$ + $$\sqrt{\sin }$$

across · Answer

Do you know what the chain rule is?

anonymous · Answer

Hi across,

Yes I do and that's what I've been using.  The problem is that I'm getting the incorrect answer EVERY TIME.  It probably has to do with the sqrt ( [...]^1/2 ) and it being incorrectly used in the equation.

I've got about 10 problems left on my homework, but I don't want to move on until I get the right answer (it's odd answer in back of book, so no credit).

across · Answer

Notice that this function can be rewritten as$$f(x)=g(h(x))+h(g(x)),$$where$$g(x)=sin(x)$$and$$h(x)=\sqrt{x}.$$I hope that makes you see the application clearer.

anonymous · Answer

Woah!  Give me one second to process that.  That looks like it may be what I've been looking for!

anonymous · Answer

How in the heck did you get this formula?  I read the section last night and didn't see this anywhere...

across · Answer

You can come up with it by simple observation... and years upon years of math. -.-

If you have any question, let me know.

anonymous · Answer

Will do.  Thanks a bunch, across!