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Question of differentiation:dy/dx where y=sin(x+y).Please solve

Question of differentiation:dy/dx where y=sin(x+y).Please solve
 

Grade:11

2 Answers

Ujjwal Sharma
35 Points
6 years ago
As here x and y are quite difficult to saperate we will get answer in terms of y.......... differentiation of this can be done using chain rule.(differentiation of y=dy/dx)  
dy/dx=[cos(x+y)]{1+(dy/dx)}
first i went on to differentiate sin(x+y)  and then i went on to differntiate what was inside the sine function.. i.e. x+y...... simply multiply them as per the product rule.
you can get further answer by rearranging.
dy/dx=[cos(x+y)]/{1-cos(x+y)}
 ALL THE BEST..... TRY TO DO SOME MORE QUESTIONS OF THIS TYPE AND YOU WILL BE ON TRACK WITH THIS CONCEPT.
Vikas TU
14149 Points
6 years ago
The simple rule would be by applying chain rule:
dy/dx => cos(x+y)*(1 + dy/dx)
on rearranging we get,
dy/dx=[cos(x+y)]/{1-cos(x+y)}.
This would be the final diffrenetiaiton.
 

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