What is the implicit derivative of 1=tanyx-y^21=tanyx−y2?
1 Answer
Sep 28, 2017
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/dx⇒2ydydx=ysec2(yx)+xsec2(yx)dydx
rArr2ydy/dx-xsec^2(yx)dy/dx=ysec^2(yx)⇒2ydydx−xsec2(yx)dydx=ysec2(yx)
rArrdy/dx(2y-xsec^2(yx))=ysec^2(yx)⇒dydx(2y−xsec2(yx))=ysec2(yx)
rArrdy/dx=(ysec^2(yx))/(2y-xsec^2(yx))⇒dydx=ysec2(yx)2y−xsec2(yx)