Question

Find the derivative

Answer 1

\[f(x)=\sqrt{x+\sqrt{x+\sqrt{x}}}\]

Answer 2

Chain rule
\[\frac{ 1 }{ 2 }(x+\sqrt{x+\sqrt{x}})^{-0.5} (1+\frac{ 1 }{ 2 }(x+\sqrt{x})^{-0.5})(1+\frac{ 1 }{ 2 }x ^{-0.5})\]

Answer 3

have you set it up with the chain rule there? i find this problem very confusing to write out.

Answer 4

Its general power rule

Answer 5

\[y^2=x+\sqrt{x +\sqrt{x}}\]
\[(y^2-x)^2=x+\sqrt{x}\]
do you know implicit

Answer 6

yes we started them in class - but, i don't think this part of my assignment has to do with implicit.

Answer 7

i tried writing this once before in latex, and it took me like twenty minutes
keep using the chain rule

Answer 8

\[\frac{1}{2\sqrt{x+\sqrt{x+\sqrt{x}}}}\] times the derivative of \[x+\sqrt{x+\sqrt{x}}\]

Answer 9

good luck writing it out, but it is a lot easier with pencil and paper

Answer 10

\[\frac{ 1 }{ 2f(x) }[f(x)^']^2\]
is this what it means

Answer 11

@satellite73

Answer 12

no i mean
\[\frac{d}{dx}[\sqrt{f(x)}]=\frac{f'(x)}{2\sqrt{f(x)}}\]

Answer 13

i have it figured out! thank youuuu.