Question

f(x)=x^(x/2)
what is f'(x)?

Answer 1

\[f(x)=x^{x/2}\]

Answer 2

Oh this is a nice one. Do you know logarithmic differentiation?

Answer 3

say y=x^(x/2)
ln y =x/2 lnx
d(ln y)=d(x ln x)/2
y'/y=1/2 * (ln x+x*1/x)
y'/y=1/2*(ln x+1)
y'=y/2 * (ln x+1)
y'=x^(x/2)*(ln x+1)

Answer 4

Sorry, I shouldn't post the answer right away. But I hope this helps :)

Answer 5

And i missed our 1/2 at the final answer.

Answer 6

@imron07 you forgot the 1/2 in the final result.

Answer 7

hehe, thanks @gezimbasha

Answer 8

thanks. but how did
d(ln y)= y'/y ?

Answer 9

Actually, d(ln x)/dx =1/x
For u(x), use chain rule:
d(ln u)/dx=1/u * du/dx =u'/u

Answer 10

oh. ok. thanks. :)

Answer 11

Okay :)