how would you figure out the derivative of ln^7(x)?

Answer 1

Use the chain rule [derivative of the outside times derivative of the inside to get:
(7(ln x)^6)*(1/x)

Answer 2

We have the 7th power of the ln function, Using the rule for diffrenetiating powers and the cain rule , we get

(ln^7(x)' = 7 ln^6(x) * 1/x, =7 ln^6(x) /x, since the derivative of ln(x) is 1/x.

Answer 3

Just how you would have done d/dx of (x+1)^7 which gives you, 7(x+1)^6

Now, for this ques, you get, [7 ln^6(x)]/x

Answer 4

I think you want the derivative of: y = ln^7(x) = [ln(x)]^7. If so you may take u = ln(x).

Then (i) du/dx = 1/x,

(ii) y = u^7, and

(iii) dy/du = 7u^6 = 7[ln(x)]^6

So that by Chain Rule:

dy/dx = [dy/du]*[du/dx] = 7[ln(x)]^6*(1/x).

Answer 5

7 * ln^6(x) / x by the chain rule

Answer 6

d/dx{ln[x]}^7 = 7{ln[x]}^6 d/dx{ln[x]} = (7/x){ln[x]}^6

Answer 7

y = ln^7(x)

y = 7ln x

dy= 7dx/x

Answer 8

d/dx (ln^7(x)) =
d(ln(x))/d(ln(x)) d/dx (ln^7(x)) =
d(ln(x))/dx d/d(ln(x)) (ln^7(x)) =
1/x 7 ln^6(x) =
7ln^6(x) / x

Answer 9

get rif of the 7.by base changing rule.
then the ans is 1/(x) * d/dx (x)
=)

Answer 10

2ln7(x)/x