Thread: Fairly basic natural logs question

Returning to differentiation after a fairly long break and presented with three questions. I'm sure there's a simpler way to do them, but I can't figure it out?

1. y(x) = ln[(f(x)+g(x))^2] => y(x) = ln[(u)^2]
y'(x) = 1*[2(f'(x)+g'(x))] / (f(x)+g(x))^2


2. y(x) = ln(x^a + zx)/(e^x*e^z)
y(x) = ln (u)/(v)
y'(x) = (V) / (U) * (V)(U') / (U)(V')
y'(x) = (V)(U)(V') / (U)(V)(U')

If that makes sense?

3. y(x) = f(g(x).u(z))
y'(x) = (g(x).u(z)).(g'(x))

Sorry if this seems a bit retarded, I'm finding the textbook a bit lacklustre in parts (Chiang / Wainwright) and statistics is much more my forte!

1.



2.



3.

Originally Posted by skeeter

1.

I thought with natural logs, the derivative of e.g. => ? I.e. it's the derivative over the original?

Re: #3, oops. it's the chain rule applying to the product rule, so I see why the answer is that.

Cheers!

Originally Posted by kedaha

I thought with natural logs, the derivative of e.g. => ? I.e. it's the derivative over the original?

Re: #3, oops. it's the chain rule applying to the product rule, so I see why the answer is that.

Cheers!

... sorry, transposed the prime