Q. 13

Differentiate the following with respect to x:

a0 xn + a1 xn – 1 + a2 xn – 2 + ……. + an – 1 x + an

Answer :

Given,


f(x) = a0 xn + a1 xn – 1 + a2 xn – 2 + ……. + an – 1 x + an


we need to find f’(x), so differentiating both sides with respect to x –


(a0 xn + a1 xn – 1 + a2 xn – 2 + ……. + an – 1 x + an)


Using algebra of derivatives –


f’(x) =


Use the formula:


f’(x) = a0 n xn – 1 + a1 (n – 1) xn – 1 – 1 + a2(n – 2) xn – 2 – 1 + ……. + an – 1 + 0


f’(x) = a0 n xn – 1 + a1 (n – 1) xn – 2 + a2(n – 2) xn – 3 + ……. + an – 1


f’(x) = a0 n xn – 1 + a1 (n – 1) xn – 2 + a2(n – 2) xn – 3 + ……. + an – 1


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