If `y=(1)/(3x^(3))` then prove that `3y+x(dy)/(dx)=0`. – InterviewSolution

InterviewSolution

1.	If `y=(1)/(3x^(3))` then prove that `3y+x(dy)/(dx)=0`.
Answer» `y=(1)/(3x^(3))=(1)/(3).x^(-3)` `rArr (dy)/(Dx)=(d)/(dx)((1)/(3)x^(-3))` `=(1)/(3)(d)/(dx)(x^(-3))=(1)/(3)(-3)x^(-4)=-x^(-4)` Now L.H.S. `=3y+x(dy)/(dx)` `=3.(1)/(3x^(3))+x(-x^(-4))` `=(1)/(x^(3))-(1)/(x^(3))=0=` R.H.S.

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