Question

find the derivative of the function
y=1n 3sqrt(x-1/x+1
(fan & award best answer)

Answer 1

What?

Answer 2

What??????????

Answer 3

thanks !! [:

Answer 4

np, do you know how to solve it from here?

Answer 5

i think s im working on a another problem and come back to it

Answer 6

@FibonacciChick666 no i dont know how to finish it

Answer 7

Why would you use u-sub? You need to know derivatives before you use u-sub for integration

Answer 8

You can apply your log rules from algebra to split everything up

Answer 9

I believe that 3 square root should be read as the cube root from what I have seen from other posters.

Answer 10

ln(ab) = ln(a) + ln(b)

Answer 11

And if so, \[y=\ln \sqrt[3]{\frac{ x-1 }{ x+1 }} \]
can be simplified to by rules of natural logs to
\[y=\frac{ 1 }{ 3 }\ln \frac{ x-1 }{ x+1 }\] which can then be further simplified by natural logs to
\[y=\frac{ 1 }{ 3 }\ln(x-1)-\frac{ 1 }{ 3 }\ln(x+1)\]

Now, if we take the derivative of y with respect to x, we get

\[\frac{ dy }{ dx }=\frac{ 1 }{ 3(x-1) }-\frac{ 1 }{ 3(x+1) }\]

This can be further simplified by algebra to:

\[\frac{ x+1-(x-1) }{ 3(x+1)(x-1) }\]

Finally, combining like terms in the numerator, we get:

\[\frac{ 2 }{ 3(x+1)(x-1) }\]

Answer 12

Follow @calmat01 method. He has it down.

Answer 13

ok so how to solve this problem: (I disagree with calmat01's answer.)
First let me restate the question:
\[y=ln(3((x−1)/(x+1))^{.5})\]

Now first rule of natural logs. You can take the exponent down and multiply it in front. So we have:
\[y=0.5*ln(3((x−1)/(x+1))\]
Second rule of logs. A quotient can be rewritten as a subtraction. So we have:
\[y=0.5*[ln(3(x−1))-ln(x+1)]\]
Next we do u,v substitution.
let u=3x-3
du=?
v=x+1
dv=?

Can you please compute these derivatives and see if you can finish the problem from this step?

\[y=0.5*[ln((u)-ln(v)]\]

Answer 14

You basically did the same thing as calmat except you used substitution which I think makes it more confusing when computing derivatives of natural log functions.

Answer 15

You are required to use substitution because it is not of the standard form. You also do not make the 3 a cube root; therefore the answer is wrong.

Answer 16

then again, I also interpreted the original question as 3 times the square root not a cube root.

Answer 17

I was basing my approach to the problem by what I have seen using the equation editor. In the equation editor, problems written in the form a root x become \[\sqrt[a]{x}\] which is how I interpreted his question.