Question

Implicit differentiation sin(x+y)=xy

Answer 1

Im stuck where I have \[(1+\frac{ dy }{ dx })-x \frac{ dy }{ dx }=y+x \frac{ dy }{ dx }\]

Answer 2

sin(x+y)=xy
or, cos(x+y) . [ 1+ dy/dx ] = x dy/dx + y

Answer 3

Ya thats what I ment

Answer 4

I dont know what to do from here exactly in cos(x+y) [1+dy/dx]= x dy/dx + y

Answer 5

or, cos(x+y) + cos(x+y) dy/dx = x dy/dx + y
or, cos(x+y) dy/dx - x dy/dx = y - cos(x+y)
or, dy/dx {cos(x+y) - x} = y - cos(x+y)
or, dy/dx = [ y - cos(x+y) ] / [ cos(x+y) - x ].................. Ans.

Answer 6

The last one

Answer 7

differentiation of sin(x+y) is :-

cos(x+y) . [ 1+ dy/dx ]

Answer 8

right

Answer 9

Yes the Last one [ y - cos(x+y) ] / [ cos(x+y) - x ] is the answer :)

Answer 10

Thanks for the help :)