Ex 12.2, 6 - Chapter 12 Class 11 Limits and Derivatives
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Ex 12.2, 6 Find the derivative of xn + axn-1 + a2xn-2+….+ an-1 x + an for some fixed real number a. Let f (x) = xn + axn – 1 + a2xn – 2+….+ an – 1 x + an (where a is constant) f’ (x) = xn + axn – 1 + a2xn – 2+….+ an – 1 x + an′ = n . xn – 1 + a(n – 1)x(n – 1) – 1 + a2 (n – 2)x (n – 2) – 1 + … …. + an – 1 . (1)x1 – 1 + 0 = nxn – 1 + a(n – 1)xn – 2 + a2 (n – 2)x n – 3 + … + an – 1 (1)(1) = nxn – 1 + a(n – 1)xn – 2 + a2 (n – 2)x n – 3 + … + an – 1 ∴ f’(x) = nxn – 1 + a(n – 1)xn – 2 + a2 (n – 2)x n – 3 + … + an – 1
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