Find the derivative of xⁿ+axⁿ-1}+a² xⁿ-2} + ...

NCERT Class XI Mathematics - Limits and Derivatives - Solutions

Question : 38 of 72

Marks: +1, -0

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.

Solution:

Let f (x) =

x^n+ax^{n-1}+a^2 x^{n-2}

+ ... +

a^{n-1} x+a^n

... (i)

Differentiating (i) with respect to x, we get

f' (x) =

nx^{n-1} + (n-1)ax^{n-2}

+ ... +

a^{n-1}

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