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Question
If xm . yn = (x + y)m+n, prove that `("d"^2"y")/("dx"^2)` = 0
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Solution
Given that: `"dy"/"dx" = y/x`
Differentiating both sides w.r.t. x
`"d"/"dx"("dy"/"dx") = "d"/"dx"(y/x)`
⇒ `("d"^2y)/("dx"^2) = (x* "dy"/"dx" y*1)/x^2`
= `(x * y/x - 1)/x^2` .....`[because "dy"/"dx" = y/x]`
= `(y - y)/x^2`
= `0/x^2`
= 0
Hence, `("d"^2y)/("dx"^2)` = 0.
Hence proved.
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