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Matthew071

  • 2 years ago

Implicit differentiation sin(x+y)=xy

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  1. Matthew071
    • 2 years ago
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    Im stuck where I have \[(1+\frac{ dy }{ dx })-x \frac{ dy }{ dx }=y+x \frac{ dy }{ dx }\]

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

  3. Matthew071
    • 2 years ago
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    Ya thats what I ment

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

  5. goformit100
    • 2 years ago
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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.

  6. Matthew071
    • 2 years ago
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    The last one

  7. goformit100
    • 2 years ago
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    differentiation of sin(x+y) is :- cos(x+y) . [ 1+ dy/dx ]

  8. Matthew071
    • 2 years ago
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    right

  9. goformit100
    • 2 years ago
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    Yes the Last one [ y - cos(x+y) ] / [ cos(x+y) - x ] is the answer :)

  10. Matthew071
    • 2 years ago
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    Thanks for the help :)

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