Question

find DY/DX by implicit differentiation : cosxy +x^6 = y^6

Answer 1

\[[(-\sin(xy)) \times (x(dy/dx)+y)] + 6x^5 = 6y^5(dy/dx)\]
\[(-xsin(xy) \times dy/dx)-ysin(xy) + 6x^5 = (6y^5 \times (dy/dx))\]
\[(-xsin(xy) \times (dy/dx)) - (6y^5 \times (dy/dx)) = ysin(xy)-6x^5\]
\[(dy/dx)[-xsin(xy)-6y^5]=ysin(xy) - 6x^5\]

Answer 2

\[dy/dx = (ysin(xy) - 6x^5)/(-xsin(xy) - 6y^5)\]
\[dy/dx = -(ysin(xy) - 6x^5)/(xsin(xy) + 6y^5)\]
\[dy/dx = (-ysin(xy) + 6x^5)/(xsin(xy) + 6y^5)\]

Answer 3

that's the best I can do. If you can, please check and/or verify the workings. Hope this might help you.

Answer 4

wouldn't the correct answer be :

-sin(xy) (x dy/dx +y) +6x^5-6y^5dy/dx
-sin(xy)(xy'+y)+6x^5-6y^5 y'
-xsin(xy)y'-ysin(xy)+6x^5-6y^5y'
+ysin(xy)+6x^5
ysin(xy)-6x^5=-xsin(xy)y'-6y^5 y'
y'=(-ysin(xy)-6x^5)/ (-xsin(xy)-6y^5

Answer 5

nevermind ur right i carried the wrong one out to the other side XP