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Find the derivative of x5 (3 – 6x–9). - Mathematics

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Question

Find the derivative of x⁵ (3 – 6x^–9).

Sum

Solution

Let f (x) = x⁵ (3 – 6x^–9)

By Leibnitz product rule,

f'(x) = $x^{5} \frac{d}{d x} (3 - 6 x^{- 9}) + (3 - 6 x^{- 9}) \frac{d}{d x} (x^{5})$

= 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

= $15 x^{4} + \frac{24}{x^{5}}$

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The Concept of Derivative - Algebra of Derivative of Functions

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Q 9.4 Q 9.3 Q 9.5

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

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NCERT Mathematics [English] Class 11

Chapter 13 Limits and Derivatives
Exercise 13.2 | Q 9.4 | Page 313

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