Question

Find the derivative of

Answer 1

\[\huge y=\sqrt{\sin \sqrt{x}}\]

Answer 2

@ganeshie8

Answer 3

chainz :>

Answer 4

yea i know that is chain rule

Answer 5

obviously but i have to apply it here @tkhunny

Answer 6

Sure you do. What's this \(\dfrac{d}{dx}\sqrt{x} =\;\)??

Answer 7

Okay...somehow, you have to pinpoint what I like to call the outer shell function :)

The function... that covers all the others...

Answer 8

I think THIS part of the function looks like a shell... don't you? :)
\[\Large \color{red}{\sqrt{\color{black}{\sin \sqrt x}}}\]

Answer 9

yes

Answer 10

Well, here's how it works... just differentiate the 'shell' as if whatever's inside is just a big fancy x...first....

now, what is the derivative of 'square root'? ^^

Answer 11

of root x ?

Answer 12

yeah, that...

Answer 13

1/2root x

Answer 14

Okay, so the first piece is \(\dfrac{1}{2\sqrt{sin(\sqrt{x})}}\). What's next?

Answer 15

^okay, as much as I'd like to say that's it, that's not it :D

After you differentiate the 'outer shell', you then multiply that entire expression by the derivative of WHATEVER WAS INSIDE that shell thingy...

So inside the outermost radical is a \(\large \sin \sqrt x\)
So what's the derivative of that?

(lawlz chain rule again)