Matthew071
Implicit differentiation sin(x+y)=xy



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Matthew071
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Im stuck where I have \[(1+\frac{ dy }{ dx })x \frac{ dy }{ dx }=y+x \frac{ dy }{ dx }\]

goformit100
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sin(x+y)=xy
or, cos(x+y) . [ 1+ dy/dx ] = x dy/dx + y

Matthew071
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Ya thats what I ment

Matthew071
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I dont know what to do from here exactly in cos(x+y) [1+dy/dx]= x dy/dx + y

goformit100
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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.

Matthew071
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The last one

goformit100
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differentiation of sin(x+y) is :
cos(x+y) . [ 1+ dy/dx ]

Matthew071
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right

goformit100
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Yes the Last one [ y  cos(x+y) ] / [ cos(x+y)  x ] is the answer :)

Matthew071
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Thanks for the help :)