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यदि (If) `xsqrt(1+y)+ysqrt(1+x)=0`, सिद्ध करें कि `(dy)/(dx)=-(1+x)^(-2)`

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दिया है ,`xsqrt(1+y)=-sqrt(1+x)`
या `x^(2)(1+y)=y^(2)(1+x)` या, `x^(2)-y^(2)=xy(y-x)`
या `x+y=-xy` या `y(1+x)=-x` …(1)
दोनों तरफ x के सापेक्ष अवकलित करें पर हमें मिलता है,
`y*1+(1+x)(dy)/(dx)=-1` या, `(1+x)(dy)/(dx)=-(y+1)`
या `(dy)/(dx)=-((y+1)/(1+x))=-(((-x)/(1+x)+1))/(1+x)` [(1) से]
`=-(-x+1+x)/((1+x)^(2))=-(1+x)^(-2)`

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