Question

find the first derivative of..

Answer 1

:O super tough

Answer 2

like a chain rule within a chain rule within a chain rule

Answer 3

let this as
\[y = (1+ x ^\frac{ 1 }{ 2 })^{\frac{ 1 }{ 2 }}\]

Answer 4

Then apply chain rule.

Answer 5

\[\frac{ d y }{ d x } = \frac{ 1 }{ 2 } ( 1 + \sqrt{x} )^{\frac{ 1 }{ 2 } - 1 } \times ( 0 + \frac{ d \sqrt x }{dx })\]

Answer 6

then do the same for the sqrtx inside the bracket again

Answer 7

\[y' = \frac{ 1 }{ 2 } (1+x \frac{ 1 }{ 2 })^{\frac{ -1 }{ 2 }}(\frac{ 1 }{ 2 }x ^{\frac{ -1 }{ 2 }})\]
tell me if you can't simplify.