Question

Differentiate the function: y=ln(lnx^3)

Answer 1

do u know differentiation by substitution? u need that to solve this prob.

Answer 2

Can you guide me through it?

Answer 3

ok put z=lnx^3, then y=lnz right?

Answer 4

Where did you get z?

Answer 5

i just pick it because z=lnx^3 will make the differentiation simpler :)

Answer 6

okay

Answer 7

what is dy/dz then?

Answer 8

Do you want me to actually put the dy/dz?

Answer 9

Wait never mind. dz=3/x and dy=1/x

Answer 10

Hahaha smart lady :P

Yes I do want to calculate dy/dz because....

in the next step, we will use differentiation by substitution so that dy/dx=dy/dz * dz/dx

Answer 11

wait y=lnz so dy/dz=?

Answer 12

1/x/3/x?

Answer 13

i think u are jumping ahead here....

y=lnz so dy/dz=1/z okay?

Answer 14

okay

Answer 15

Then like I said by substitution, dy/dx=(dy/dz)*(dz/dx) ok?

Answer 16

ok

Answer 17

so we already have dy/dz=1/z=1/lnx^3=1/(3*lnx) so we need to calculate dz/dx okay?

Answer 18

okay

Answer 19

z=ln(x^3) what is dz/dx?