Bignose - calculus

[MIKE1218]

This seems straightforward, but it's a multiple choice question and my answer is not one of the choices.

What is the derivative of y=ln(1-x^2)^(1/2)

If anybody can help before Bignose sees this please feel free.

Thanks!

 

[Wi-Golfer]

y = ln(1-x^2)^(1/2) is the same as

(1/2) ln(1-x^2). Differentiating using the chain rule and noting that d(ln x)/dx = 1/x, we get

1/2 * 1/(1-x^2) * 2x = x/(1-x^2).

 

[MIKE1218]

That's what I got, but that's not one of the choices. Curious. Thanks for verifying my answer.

 

[Bignose]

y = ln(1-x^2)^(1/2) is the same as

(1/2) ln(1-x^2). Differentiating using the chain rule and noting that d(ln x)/dx = 1/x, we get

1/2 * 1/(1-x^2) * 2x = x/(1-x^2).

This is spot on if it is ln ( (1-x^2)^(1/2)) That is, the natural log of the square root of 1-x^2. But, it is a little different if it is the square root of the natural log of 1-x^2. It is usually the first, but it is good to make sure exactly what you are aiming for.

Wi has it exactly right, however. Use the chain rule and the definition of the derivative of ln. (Using the properly of logarithms to move the exponent of the term having the logarithm taken of it is a good move, too, though using the chain rule, you should get the same answer.)

Edited to add: Wi has one small error. He dropped a minus sign: d/dx of (1-x^2) = -2x, not just 2x.

 

[Wi-Golfer]

I don't know if that's correct or not, stole the answer off Yahoo

 

[MIKE1218]

I didn't even see that mistake, I just assumed he meant -x/(1-x^2), which is what I got.

-x/(1-x^2) is not a choice nor is x/(x^2 -1)

I'm not sure what's going on here.

 

[Wi-Golfer]

Will have to go & scold Yahoo, can't count on the net for anything except quality porn now days:thumbs up:

 

[Bignose]

Is -x/(1-x^2) close to anything? Or is an answer -x/(sqrt{ln(1-x^2)}*(1-x^2) ? (That second one is is derivative if the ^(1/2) is on the outside of the ln.

Otherwise, there is just a typo in something. Either the answers or the question.

 

[MIKE1218]

-x/(x^2-1) is a choice. The others are not close. Must be a typo. Thanks!

 

[TheWOAT]

1/2 ln (1-x2)

1/2 (1-x2)(-2x)

-x/(1-x2)

After you diff. the ln(x), you must also diff the 'x', or whats in the parathesis..
the derivative of 1-x2 is -2x, which gets multiplied to the rest of the function