Question

f(x,y)=sin inverse (y/x).|x|>|y| i want to differentiate by x.

Answer 1

retype question:
\[f(x,y)=\sin^{-1}\frac{y}{x}\]

Answer 2

i got this answer:\[-\frac{y}{x \sqrt(x^2-y^2)}\]

Answer 3

but the answer in book is:\[-\frac{|x|y}{x^2 \sqrt(x^2-y^2)}\]

Answer 4

@eamier

Answer 5

yes

Answer 6

wait a second...

Answer 7

if i substitute x by value like 2 or -2 its answer is same.. so why we need |x|

Answer 8

by definition...
\[\left| x \right|=x,x>0\]
and -x,x<0

Answer 9

but in the numerator , you actually get \(\sqrt {x^2}\) , right ?
which you wrote it as x, isn't it.
actually \(\sqrt {x^2}=|x|\)

Answer 10

yes i see..

Answer 11

\(\sqrt {\dfrac{ {x^2-y^2}}{x^2}}=\dfrac{\sqrt{x^2-y^2}}{|x|}\)
ok :)

Answer 12

thank you..

Answer 13

welcome ^_^