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Mathematics 18 Online
OpenStudy (anonymous):

implicit differentiation xsiny+ysinx=0 can somebody help @Writing

OpenStudy (anonymous):

Does't belong in writing.

OpenStudy (anonymous):

siny+x(cosy)(dy/dx) +v(dy/dx)(sinx)+ycosx

OpenStudy (anonymous):

you then need to solve for dy/dx

OpenStudy (anonymous):

can u put it in prime notation

OpenStudy (anonymous):

also disregard that v I put in there. It was an accident. Nothing goes where that v is.

OpenStudy (anonymous):

\[\sin(y)+x\cos(y)y'+y'\sin(x)+y\cos(x)=0\]

OpenStudy (anonymous):

via the product rule. solve for \[y'\]

OpenStudy (anonymous):

this is exactly what december wrote, just used y' instead of dy/dx

OpenStudy (anonymous):

If you want it solved, you just need to use basic algebra to get x(cosy)y'+y'sinx =-siny-ycosx. Proceed to factor out a y' to get y'(xcosy+sinx) = -siny-ycosx Then divide by xcosy+sinx to get y' = (-siny-ycosx)/(xcosy+sinx) If you do not understand implicit differentiation, you should probably study more. It is a very simple process that is barely any different than normal differentiation.

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