Letf(x) = (2a² – 8)° (5z' + 8)6.8) 13|.f'(æ) =Question Help: Message instructorSubmit Ouestionump tn And

Given: fx=2x2-865x2+813 differentiating on both sides f'x=ddx2x2-865x2+813…

Answered: Let f(x) = (2a² – 8) (5æ + 8) 13 %3D…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Given:

$f (x) = {(2 x^{2} - 8)}^{6} {(5 x^{2} + 8)}^{13}$

differentiating on both sides

$f' (x) = \frac{d}{d x} ({(2 x^{2} - 8)}^{6} {(5 x^{2} + 8)}^{13})$

$= \frac{d}{d x} [{(2 x^{2} - 8)}^{6}] \cdot {(5 x^{2} + 8)}^{13} + {(2 x^{2} - 8)}^{16} \cdot \frac{d}{d x} [{(5 x^{2} + 8)}^{13}]$

$= 6 {(2 x^{2} - 8)}^{5} \cdot \frac{d}{d x} (2 x^{2} - 8) \cdot {(5 x^{2} + 8)}^{13} + {(2 x^{2} - 8)}^{6} \cdot 13 {(5 x^{2} + 8)}^{12} \cdot \frac{d}{d x} [5 x^{2} + 8]$

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Let f(x) = (2a² – 8) (5æ + 8) 13 %3D f'(x)