Question

Basic Calculus: Derivation

Answer 1

did u want someone to assign u a problem?!

Answer 2

\[\tan(\tan(\tan(x)))\]

Answer 3

chain rule. are you familiar with it?

Answer 4

derivative of the outside times the derivative of the inside.

Answer 5

Is this right?\[\sec^2(\tan(\tan(x)))\sec^2(\tan(x))\sec^2(x)\]

Answer 6

yes.

Answer 7

how about the derivative of \[x^x\]

Answer 8

@Ashleyisakitty

Answer 9

assume it to be u den take log on both sides and solve....

Answer 10

@vedic like this? \[\log(u)=\log(x^x)\]

Answer 11

final answer would be \[x^x (1+logx)\]

Answer 12

yup ryt...:)

Answer 13

and what's next?

Answer 14

log (a^b) = b loga

so log(x^x) becomes x logx

Answer 15

so our eqtn becomes logu=xlogx and now differentiating both sides with respect to x..

Answer 16

\[\log(u)=xlog(x)\] log(u) is just a number?

Answer 17

let \[u=x^x\]
taking log on both sides,
\[logu= xlogx\]
diff. both sides w.r.t to x,
\[(1/u)*(du/dx) = (x/x) +(1* logx)\]

Answer 18

log u is another variable..... not a number...

Answer 19

understood???

Answer 20

yeah, thanks so the answer \[\frac{ 1 }{ u }=\frac{ x }{ x }+\log(x)\rightarrow u=1+\frac{ 1 }{ \log(x) }\]like this?

Answer 21

@vedic

Answer 22

no whn u differentiate one variable with respect to other u get (du/dx) term also....

Answer 23

chck my above reply i hv mntioned it der....

Answer 24

ok thanks a lot