Question

find the derivative:

Answer 1

\[y=x ^{x ^{2}}\]

Answer 2

so far i have
\[x ^{2}(x)^{x ^{2}-1}(1)\]

Answer 3

dy/dx=x^2(x^(x^2-1)
=

Answer 4

thats what i have written already

Answer 5

no x is a variable

Answer 6

huh?

Answer 7

you are right thats the derivative

Answer 8

so is the answer: \[x ^{x ^{2}+1}\]

Answer 9

?

Answer 10

\[y = x ^{x ^{2}}=\exp(x ^{2}.\ln (x))\]

Answer 11

and now you can derive

Answer 12

why are you changing it to a natural log?

Answer 13

it seems like youre making it more complicated than it has to be.

Answer 14

when you have \[y=x ^{n} \]

Answer 15

the condition to derive like that \[n.x ^{n-1}\]

Answer 16

look up to see what i have already written down

Answer 17

is that n is constant.

Answer 18

yes I've seen what you've written

Answer 19

and it's false because the power isn't constant

Answer 20

if u take na log then u should also take nalog y then it become more complicated

Answer 21

so how do i start the problem? take ln of both sides?

Answer 22

so when you have something like that \[y = f(x)^{g(x)}\]

Answer 23

\[lny=x^2 lnx\]

Answer 24

you must first write it \[y = \exp ( g(x).\ln (f(x))\]

Answer 25

is what i wrote juts above you right?

Answer 26

no you don't have to do this ((\[lny=x ^{2}\ln(x)\]

Answer 27

you know how to derive this \[\exp(f(x))\]

Answer 28

????

Answer 29

\[(\exp(u))'=u'\exp(u)\]

Answer 30

yes

Answer 31

for you u = x²ln(x) it's OK??

Answer 32

u'= 2xln(x) + x³ . 1/x

Answer 33

excuse it's \[u'=2xln(x) + x ^{2}\times \frac{ 1 }{x }\]

Answer 34

you follow me ??