Q. 13

# Differentiate the following with respect to x:a0 xn + a1 xn – 1 + a2 xn – 2 + ……. + an – 1 x + an

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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