Find the derivative of x–4 (3 – 4x–5). - Mathematics

Question

Find the derivative of x^–4 (3 – 4x^–5).

Sum

Solution

Let f(x) = x^–4 (3 – 4x^–5)

By Leibnitz product rule,

f'(x) = $x^{- 4} \frac{d}{d x} (3 - 4 x^{- 5}) + (3 - 4 x^{- 5}) \frac{d}{d x} (x^{- 4})$

= x^-4 {0 - 4 (-5) x^-5-1} + (3 - 4x^-5) (-4) x^-4-1

= x^-4 (20x^-6) + (3 - 4x^-5) (-4x^-5)

= 20x^-10 + 12x^-5 + 16x^-10

= 36x^-10- 12x^-5

= $- \frac{12}{x^{5}} + \frac{36}{x^{10}}$

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The Concept of Derivative - Algebra of Derivative of Functions

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Chapter 13: Limits and Derivatives - Exercise 13.2 [Page 313]

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Find the derivative of x–4 (3 – 4x–5). - Mathematics

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