Question

Differentiate: y=cscxln(x^6/2x-1)
I know the answer is y'=-cscxcotxln (x^6/2x-1) + cscx (6/x - 2/2x-1)
I'm not sure how the last set of parenthesis came about, I thought the derivative would be 6x^5.

Answer 1

I answer you the last part only, is it ok?

Answer 2

that is ln (x^6 / 2x-1) = ln x^6 - ln (2x -1) . when you take derivative,
\[(ln x^6)' =\]\[\frac{ 1 }{ x^6 }(6x^5)=\frac{ 1 }{ x }\] the same with the second part. so that's why you have it. :)

Answer 3

Then why in the final answer is it (6/x)-(2/2x-1) ?

Answer 4

ok, the second part is (ln (2x-1))' = \[\frac{ 1 }{ 2x-1 }(2x-1)' = \frac{ 2 }{ 2x -1 }\]
now combine them, ( let ....... csc x* aside, just calculate the last part is (ln (x^6/ 2x -1) )'
as I calculate above, the derivative of that ln = (6/x) -(2/2x-1) .
just write that answer after cscx* (.....) you have yours
got it?

Answer 5

Ahh gotcha thanks :)

Answer 6

ok, you must be something, I give out the shortcut and you got it quickly. :)

Answer 7

I figured out the first part my brain just fizzled at the end. But thank you :) It's finals week lol