Question

if y=xln^3x, then dy/dx =?

Answer 1

\[xln^3x\]

Answer 2

Woops no, ;careful esama :O
if the power is being applied to the log, we can't use that rule.

Only when the power is being applied to the contents of the log is that true.

Answer 3

yes @zepdrix
a'm so sorry and thank you

Answer 4

Uhhh so looks like you start with `product rule` yes kevin? :)

Answer 5

yes you do (x)*(dy/dx ln^3x) + (ln^3x)*(dy/dx x)

Answer 6

Good good.
So just having trouble differentiating the log part?

Answer 7

yes

Answer 8

when do we include log?

Answer 9

It's a composition of functions.
We'll have to apply the chain rule.

If you write it like this,\[\Large\bf\sf \frac{d}{dx}\ln^3x\quad=\quad \frac{d}{dx}(\ln x)^3\]It's a little easier to see what the outermost function is.

Answer 10

See how the outermost function is the ( )^3
we start with power rule

Answer 11

3(lnx)^2 * (dy/dx lnx)?

Answer 12

ya looks good so far!

Answer 13

Your derivative operator is d/dx
not dy/dx

just something to keep in mind

Answer 14

oh thank you for the clarification

Answer 15

(3(lnx)^2)/x

Answer 16

good :)

Answer 17

okay thank you