InterviewSolution
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InterviewSolution
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Find the derivative of `x^(n)+ax^(n-1)+a^(2)x^(n-2)+..........+a^(n-1)x+a^(n)` for some fixed real number a. |
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Answer» Let `y=x^(n)+ax^(n-1)+a^(2)x^(n-2)+.....+a^(n=1)x+a^(n)` `rArr (dy)/(dx)=(d)/(dx)[x^(n)+ax^(n-1)+a^(2)x^(n-2)+.......+a^(n-1)x+a^(n)]` `=(d)/(dx)x^(n)+a(d)/(dx)x^(n-1)+a^(2)(d)/(dx)x^(n-2)+.........+a^(n-1)(d)/(dx)x+(d)/(dx)a^(n)` `=nx^(n-1)+a(n-1)x^(n- 2)+a^(2)(n-2)x^(n-3)` `+..........+a^(n-1).1+0` `=nx^(n-1)+a(n-1)x^(n-2)+a^(2)(n-2)x^(n-3)+.....+a^(n-1)`. |
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