What is the implicit derivative of 1=tanyx-y^21=tanyxy2?

1 Answer
Sep 28, 2017

dy/dx=(ysec^2(yx))/(2y-xsec^2(yx))dydx=ysec2(yx)2yxsec2(yx)

Explanation:

"differentiate "color(blue)"implicitly with respect to x"differentiate implicitly with respect to x

"differentiate "tan(yx)" using "color(blue)"chain/product rules"differentiate tan(yx) using chain/product rules

0=sec^2(yx)xxd/dx(yx)-2ydy/dx0=sec2(yx)×ddx(yx)2ydydx

rArr2ydy/dx=sec^2(yx)(y+xdy/dx)2ydydx=sec2(yx)(y+xdydx)

color(white)(rArr2ydy/dx)=ysec^2(yx)+xsec^2(yx)dy/dx2ydydx=ysec2(yx)+xsec2(yx)dydx

rArr2ydy/dx-xsec^2(yx)dy/dx=ysec^2(yx)2ydydxxsec2(yx)dydx=ysec2(yx)

rArrdy/dx(2y-xsec^2(yx))=ysec^2(yx)dydx(2yxsec2(yx))=ysec2(yx)

rArrdy/dx=(ysec^2(yx))/(2y-xsec^2(yx))dydx=ysec2(yx)2yxsec2(yx)