Question

Log derivatives: y = e^3ln(x+1)

Answer 1

d/dx ln(u) = u' / u

Answer 2

So d/dx ln(x + 1) = ?

Answer 3

is there a log rule?

Answer 4

Also, is ln(x+1) a part of exponent or just 3?

Answer 5

ln(x+1) is a part of the exponent and 3 is the coefficient

Answer 6

Oh I see. Remember that 3ln(x+ 1) = ln(x + 1)³ and e^lnx = x

So what does e^(3ln(x+1)) equal to?

Answer 7

so what happens to the e?

Answer 8

because i did product rule for the 3ln(x+1)

Answer 9

It was removed, since e^ln(x) = x

Answer 10

Instead, use the properties of logarithm. We know that n·lnx = lnxⁿ and e^lnf(x) = f(x)

So e^(n·lnf(x)) = xⁿ

So what does e^(3ln(x+1)) equal to?

Answer 11

3(X+1)^2

Answer 12

We know that e^(3ln(x+1)) = (x+1)³

Applying chain rule: f(g(x)) = f'(g(x)) · g'(x)

Let f(x) be x³ and g(x) be x + 1.

So (x+1)³ = 3(x + 1)² · 1 = 3(x+1)²

So, you are correct, sir.

Is this clear?

Answer 13

lol yes thank you!

Answer 14

Glad I helped lol.