Why Do I Get a Different Result When Differentiating ln(x + sqrt(x^2-1))?

[UsernameValid]

How do I find the derivative of (x)=ln(x+(x^2-1)^1/2)

The answer is suppose to be 1/(x²-1). But I keep ending up with 2x/(x²-1).

 

[Mark44]

How do I find the derivative of (x)=ln(x+(x^2-1)^1/2)

Is this supposed to be f(x) = ...

The answer is suppose to be 1/(x²-1). But I keep ending up with 2x/(x²-1).

Show us what you did.

Also, do not delete the three parts of the homework template. They are there for a reason.

 

[UsernameValid]

Well, the problem says h(x).


(d/dx)ln(x+(x²-1)^1/2*(d/dx)(x+(x²-1)^1/2*(d/dx)(x²-1)^1/2*(d/dx)(x²-1).

1/(x+(x²-1)^1/2 * 1+[x/(x²-1)]^1/2 * x/(x²-1)^1/2 * 2x

Which actually gets me 2x²/(x²-1)

 

[haruspex]

(d/dx)ln(x+(x²-1)^1/2*(d/dx)(x+(x²-1)^1/2*(d/dx)(x²-1)^1/2*(d/dx)(x²-1).

I can't decipher that line. Left and right parentheses don't match up. Is there an equals sign missing? If not, I don't understand why there are any log terms in there.

 

[Mark44]

Well, the problem says h(x).

How was I to tell? You wrote this

How do I find the derivative of (x)=ln(x+(x^2-1)^1/2)

(d/dx)ln(x+(x²-1)^1/2*(d/dx)(x+(x²-1)^1/2*(d/dx)(x²-1)^1/2*(d/dx)(x²-1).

There are actually too many "d/dx" operators in there, although I get what you're trying to do. Your task is to do this differentiation:

d/dx(ln(x+(x²-1)^1/2)

$$= \frac{1}{x + (x^2 - 1)^{1/2}} \cdot d/dx(x + (x^2 - 1)^{1/2})$$
$$= \frac{1}{x + (x^2 - 1)^{1/2}} \cdot (1 + d/dx[(x^2 - 1)^{1/2}]$$
and so on, whittling away at it a little at a time.

1/(x+(x²-1)^1/2 * 1+[x/(x²-1)]^1/2 * x/(x²-1)^1/2 * 2x

Which actually gets me 2x²/(x²-1)