Question

Find the derivative:

Answer 1

\[y=4x \sqrt{x+\sqrt{x}}\]

Answer 2

OK so do u know the basic Derivation formulas??

Answer 3

Chain rule/product rule/power rule

Answer 4

\[y=4x*(x+x^{1/2})^{1/2}\]

Answer 5

I'll leave it to @bahrom7893 !!He knows wat he's doin!! -_<

Answer 6

\[y' = 4*(x+x^{1/2})^{1/2}+4x*((x+x^{1/2})^{1/2})'\]

Answer 7

So far so good?

Answer 8

Yup.

Answer 9

Okay so now let's find the following:
\[((x+x^{1/2})^{1/2})'=\frac{1}{2}(x+x^{\frac{1}{2}})^{-\frac{1}{2}} * (1+\frac{1}{2}x^{-\frac{1}{2}})\]

Answer 10

Are you still following? I'll give you a moment to let it sink in.

Answer 11

O_O!! Now dats wat I call a Derivative!!

Answer 12

Yup yup, all good here.

Answer 13

Okay, so now just substitute whatever's in the parenthesis into the previous equation, and do some simplification.

Answer 14

So answer I got \[y=\frac{6x+5\sqrt{x}}{\sqrt{x+\sqrt{x}}}\]

Answer 15

it's probably right.. sorry im too lazy to simplify.. @.Sam. can you check?

Answer 16

yup http://www.wolframalpha.com/input/?i=%284xsqrt%28x%2Bsqrt%28x%29%29%29%27

Answer 17

His answer is right out of wolf, but not sure about you @bahrom7893 xD

Answer 18

Well if it is right, then we're good to move on.

Answer 19

I didn't use Wolfram.

Answer 20

Anyways, thanks for your help guys!

Answer 21

What I've got is
\[y'=(4x)(\frac{1}{2})(x+x^{1/2})^{-1/2}(1+\frac{1}{2\sqrt{x}})+4\sqrt{x+\sqrt{x}}\]

Answer 22

For x=2, y'=10.32, you can use this as a guide in case you have any mistakes