Question

Find dy/dx : please answer it in detail, question will be posted below

Answer 1

answer in worksheet if possible =)

Answer 2

Implicit differentiation.

Answer 3

well not really, but ugly as hell

Answer 4

\[\ln(y^3)=3\ln(y)\] so you can take the derivative of the right hand side, divide by 3 and then multiply by the original mess to get dy/dx

Answer 5

anyone can upload work example?

Answer 6

i don't know how. we can maybe find the derivative of say
\[\sin^{-1}(\frac{x-1}{x+1})\] by hand it will be a pile of algebra. do you need all the work or just the solution

Answer 7

detailed solution =)

Answer 8

Well, it is cleaner to just find the derivative of both sides. LHS would be something like\[(3y ^{2}/y ^{3})(dy/dx)\]

Answer 9

left hand side is
\[\frac{3}{y}y'\] that is the easy part. that is why i said take the derivative of right hand side, divide by 3 and then multiply by y. oh but you don't know y do you? damn

Answer 10

so yeah, just multiply by y because your answer will have a y in it

Answer 11

You don't really have to find y; it would just be part of the complicated (or messy answer).

Answer 12

i mean given enough time and algebra i guess we can find the derivative of
\[\sin^{-1}(\frac{x-1}{x+1})\] but i can't imagine doing such a thing. i would use maple or at least wolfram

Answer 13

it is
\[\frac{1}{\sqrt{1-(\frac{x-1}{x+1})^2}}\times \frac{2}{(x+1)^2}\]\]

Answer 14

via the chain rule. now maybe we can do some work in the denominator

Answer 15

hell i'd leave it like that. where did this problem come from? if you want reams of algebra you can figure out why this is the same as
\[\frac{2x}{\sqrt{2x^2-x^4}}\] but i cannot do it

Answer 16

scratch that last one it is wrong!

Answer 17

wow check this out!

Answer 18

http://www.wolframalpha.com/input/?i=d%2Fdx+arcsin%28%28x-1%29%28x%2B1%29%29

Answer 19

click on "show steps" and all the gory details are there for you! every last one.

Answer 20

confused now :s what about the cot? can make it more orderly