Thread: Logarithmic Differentiation: Finding derivative

y = (x³√(x² + 1))/(x - 1)
What I did:
I used natural log on both sides.
I brought the exponents into the coefficient.
I also brought the (x - 1) up by doing it to the negative one exponent
Then I used the log properties.

So tell me if this is the correct way:
ln y = 3lnx + (1/2)ln(x² + 1) - ln(x - 1)

Then I find the derivative
1/y(dy/dx) = 3/x + (1/2)(1/(x² + 1)) - (1/(x - 1))

After that I multiplied both sides by y, then plugged in y, which is the original equation.
So would this be right?

Thanks

You made a small mistake in the derivative of ln(x²+1)^1/2 but other than that it is correct

Originally Posted by Shakarri

You made a small mistake in the derivative of ln(x²+1)^1/2 but other than that it is correct

Hmm, so first I would put the exponent into the coefficient right?
(1/2)ln(x²+1)

Um, would I then have the log go into the x and 1?
Yeah sorry, doing the derivative of 1 variable for ln is easy for me.

So if it was that (1/2)ln(x²+1)
I wouldn't just do what's in the parenthesis and put it all down under 1?
Then multiply it by 1/2?
So like 1/(2(x²​+1))?

let

Originally Posted by Shakarri

let

Oh right, now I remember!
So it's the derivative of that over the original!

Thanks!


Then after that you would multiply it by 1/2 right?
Which will be 2x/(2(x²​+1))