How do you differentiate a natural logarithm in the form y = ln(x^n+b) ?

Question

I have to do a question where I have to differentiate using the quotient rule, but I can't even differentiate part of it.
The bit I'm stuck on is differentiating y=ln(x^2+4)

Any help would be much appreciated, thanks!

Answer 1

d/dx of ln(fx)=[1/f(x)][df(x)/dx] the are math websites google differentiate

Answer 2

Let z = x² + 4
Then you have y = ln z as your function.

Apply the chain rule : dy/dx = dy/dz . dz/dx

and you should be able to do both bits of that!

Answer 3

I wan't help you and I know I can.

Unfortunately I vowed never to do any maths once I completed my Engineering degree.

It's probably the old log base e thing but I really don't want to think about it.

Sorry. Good luck.

Answer 4

Let u = x^n + b
du/dx = nx^(n-1)
y = ln u
dy/du = 1 / u
dy/dx = (dy/du) (du/dx)
dy/dx = (1/u) (nx^(n - 1))
dy/dx = nx^(n - 1) / (x^n + b)

y = ln(x² + 4)
dy/dx = 2x / (x² + 4)