Question

derivative: ln(xsqrt(x^2 - 1))

Answer 1

What is the derivative of ln(x) ??

Answer 2

1/x

Answer 3

Yep...

Answer 4

let me show my first step

Answer 5

Then do the derivative of \(x \sqrt{x^2 - 1}...\)

Answer 6

Yep carry on...

Answer 7

1/xsqrt(x^2 - 1) times d/dx (xsqrt(x^2 - 1)

Answer 8

Yep..

Good..

Answer 9

Now find the derivative of xsqrt{x^2-1} ..

Answer 10

should i first write it as x (x^2 - 1)^1/2

Answer 11

It is your wish..

But don't forget to use Product rule here..

Answer 12

so well have (x) d/dx (x^2-1)^1/2 + (x^2-1)^1/2 + d/dx (x)

Answer 13

* there instead of + right ???

Answer 14

for the product rule

Answer 15

At last you have written + there with d/dx(x) term..

Do you think that is right ??

Answer 16

oooh lol didnt see that ya ur right

Answer 17

so well now have (x) 2x 1/2(x^2-1)^-1/2 + (x^2-1)^1/2

Answer 18

Go slow need to hurry..

Answer 19

these things take time lol

Answer 20

Looks nice to me...

Answer 21

Combine both the results now..

Answer 22

and we can reduce that to 1/xsqrt(x^2-1) [x^2(x^2-1)^-1/2 + (x^2-1)^1/2]