log dif solution

[rotund hawk]

There was no sol provided. Could someone show me how to do it?

[tall crystal]

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[rotund hawk]

Maybe I did something wrong in the differentiation?

There’s just no way I’m going to get near that answer provided with what I’ve got

[azure abyss]

,rccw

[azure abyss]

don't use '×' when you're dealing with variables

[rotund hawk]

Alright

[azure abyss]

cuz '×' can be confused with x

[rotund hawk]

Yh I understand

Usually use dots or brackets innit

[azure abyss]

,calc derivative('log(sqrt(sin(x))/x)','x')

[copper arrow]

Result:

(x * cos(x) / 2 / sqrt(sin(x)) ^ 2 - 1) / x

[azure abyss]

that's how u can self-check ur work

or use wolfram alpha

you can continue by simplifying the RHS a bit

you see there's two denominators $\sqrt{\sin x}$

[copper arrow]

vin100

[azure abyss]

in the given answer you see "cot". that should come out easily after the simplificatioin

simplication*

after that you can look at the LHS

how to get "dy/dx" from "(dy/dx) / y"?

[rotund hawk]

Not a clue mate

[azure abyss]

there're 3 ways to see things in math:

1. symbolic
2. visual
3. verbal

here we're not gonna plot graph so forget number 2 for the moment

symbolic view can tell us some precise info

but sometimes it can be so abstract to human mind that it losts us

so we rephrase the math expressions in words. i.e. we switch to the verbal side a bit

• current LHS = implicit derivative / y

• target LHS: impliciat implicit derivative only

[rotund hawk]

Are you doing a bsc? Cause your maths is insane man

[azure abyss]

i did an MSc in maths

i grad a few yrs ago

[rotund hawk]

I’m doing a BSC in math and Econ next year

I’ve done all the applications

[azure abyss]

• current LHS: implicit derivative divided by y
• target LHS: implicit derivative
  it shld be obvious that we multiply current LHS by y to get target LHS