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