Question

निम्नलिखित का अवकलज ज्ञात कीजिए:

x⁵ (3 – 6x^{– 9})

Answer 1

माना f (x) = x⁵ (3 – 6x^–9)

Leibnitz गुणन सूत्र द्वारा,

f'(x) = `x^5 d/(dx) (3 - 6x^-9) + (3 - 6x^-9) d/(dx) (x^5)`

= x⁵ {0 - 6(-9)x^-9-1} + (3 - 6x^-9)(5x⁴)

= x⁵ (54x^-10) + 15x⁴ - 30x^-5

= 54x^-5 + 15x⁴ - 30x^-5

= 24x^-5 + 15x⁴

= `15x^4 + 24/x^5`