Thread: logorithmic differentiation

Heres what i did:

used the laws of logs to get this:

7x ln (sqrt(x))

ln(y) = 7x ln (sqrt(x))

start solving by implicit differentiation:

y'/y = 7x*(1/x) *(1/2sqrt(x))+ln(sqrt(x))*7

final = y'=y(7x*(1/x) *(1/2sqrt(x))+ln(sqrt(x))*7)

I think i know what i did wrong, i used ln(sqrt(x)) as 1 function instead of 2. This is a Web Assign and im about out of guesses. If I would apply the product rule between 7x and ln then apply it in another product rule with sqrt(x) would i get the right answer?

Originally Posted by Evan.Kimia

Heres what i did:

used the laws of logs to get this:

7x ln (sqrt(x))

ln(y) = 7x ln (sqrt(x))

start solving by implicit differentiation:

y'/y = 7x*(1/x) *(1/2sqrt(x))+ln(sqrt(x))*7

final = y'=y(7x*(1/x) *(1/2sqrt(x))+ln(sqrt(x))*7)

I think i know what i did wrong, i used ln(sqrt(x)) as 1 function instead of 2. This is a Web Assign and im about out of guesses. If I would apply the product rule between 7x and ln then apply it in another product rule with sqrt(x) would i get the right answer?

the equation can be further simpilifed before you take the derivative:



You could also note this from the beginning



Then take the log

So then we get

...

I hope this helps