यदि `x^(3)cos(xy)+y^(3)sin(xy)+1=0` हो तो `(dy)/(dx)` का मान होगा

Options

A. `(x^(3)ytan(xy)-(3x^(2)+y^(4)))/(xy^(3)+(3y^(2)-x^(4))tanxy)`
B. `(x^(3)ytan(xy)+(3x^(2)+y^(4)))/(xy^(3)-(3y^(2)-x^(4))tanxy)`
C. `(x^(3)y-(3x^(2)+y^(4))tan(xy))/(xy^(3)tan(xy)+(3y^(2)-x^(4)))`
D. इनमे से कोई नहीं

Answer

A

Explanation

दिए गए समीकरण का के सापेक्ष अवकलन करने पर,
`-x^(3)sin(xy){x(dy)/(dx)+y}+3x^(2)cos(xy)+y^(3)cos(xy){x(dy)/(dx)+y}+3y^(2)(dy)/(dx)sin(xy)=0`
`rArr" "{-x^(4)sin(xy)+xy^(3)cos(xy)+3y^(2)sin(xy)}(dy)/(dx)+{-x^(3)ysin(xy)+3x^(2)cos(xy)+y^(4)cos(xy)}=0`
`rArr(dy)/(dx)=-(3x^(2)cos(xy)-x^(3)ysin(xy)+y^(4)cos(xy))/(-x^(4)sin(xy)+3y^(2)sin(xy)+xy^(3)cos(xy))`
`cos(xy)` से ऊपर - नीचे भाग करने पर
`=(x^(3)ytan(xy)-(3x^(2)+y^(4)))/(xy^(3)+(3y^(3)-x^(4))tan(xy))`