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Question

If xmyn=(x+y)m+n, then which of the following is/are true :

A
dydx=yx
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B
dydx=yx
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C
d2ydx2=x2+y2x2
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D
d2ydx2=0
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Solution

The correct option is D d2ydx2=0
Given xmyn=(x+y)m+n
Applying ln both the sides
mln(x)+nln(y)=(m+n)ln(x+y)
Differentiating w.r.t x
mx+nyy=m+nx+y(1+y)
y(nym+nx+y)=m+nx+ymx
y(nxmy)y(x+y)=(nxmy)x(x+y)
y=yx(i)
Differenting w.r.t x
y′′=xyyx2=x(yx)yx2=0 from (i)
y′′=0

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