Using implicit differentiation, find y' if \sin(x + y) =

vacinammo288

vacinammo288

Answered question

2022-04-21

Using implicit differentiation, find y' if sin(x+y)=y2cos(x)

Answer & Explanation

zavesiljid

zavesiljid

Beginner2022-04-22Added 21 answers

I recommend the formal approach.
Say F(x,y)=0. Take the d of that and get dF(x,y)=0. But
dF(x,y)=Fxdx+Fydy
and so
dydx=FxFy
This is also part of the implicit function theorem.
So now F(x,y)=sin(x+y)y2cosx, so
Fx=cos(x+y)+y2sinx
Fy=cos(x+y)2ycosx
dydx=cos(x+y)+y2sinxcos(x+y)2ycosx
bobthemightyafm

bobthemightyafm

Beginner2022-04-23Added 16 answers

sin(x+y)=y2cos(x)product of 2 functions
so the derivative of the product of 2 functions is:
(f(x)g(x))=f(x)g(x)+f(x)g(x)
cos(x+y)(1+y)=2yycos(x)y2sin(x)

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