d/dx x(1+y)^(1/2) + y(1+x)^(1/2)=0. Can some1 show me the calculation because i didn't get like the answer.
[ans=-1/(1+x)^2 but my calculation=-(sqrt(y+1) (2 sqrt(x+1) sqrt(y+1)+y)/(sqrt(x+1) (2 sqrt(x+1) sqrt(y+1)+x)]
I suppose the question is to solve for y in terms of x, in which case your calculation is not in an explicit form, i.e. it is in the form y=f(x,y).
If the question is to solve for y in terms of x, i.e. the answer represents
y=-1/(1+x)^2,
It should give zero when substituted into the original equation,
d/dx [x(1+y)^(1/2) + y(1+x)^(1/2)]=0
or
d/dx [x(1+y)^(1/2)] + y(1+x)^(1/2)=0
(I do not know which case or if parentheses are missing).
Neither of them equals zero.
So it would be appropriate to check the question for missing parentheses, and the specify the context of the question (solve for y?) etc. before proceeding further.