Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Finally, use the Generalized Power Rule to determine \(\frac{d}{dx}[x^9 - x]\), noting that \(x^9 - x\) is the difference of two terms. \[ \frac{d}{dx}[(x^9 - x)^9] = 9(x^9 - x)^8 \cdot \frac{d}{dx}[x^9 - x] \] \[ = 9(x^9 - x)^8 \cdot \left( \frac{d}{dx}[x^9] - \frac{d}{dx}[x] \right) \] \[ = 9(x^9 - x)^8 \left( \text{[ ]} \right) \] Therefore, if \(f(x) = (x^9 - x)^9\), then we have the following result. \[ f'(x) = \frac{d}{dx}[(x^9 - x)^9] = \text{[ ]} \]
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Transcribed Image Text:Finally, use the Generalized Power Rule to determine \(\frac{d}{dx}[x^9 - x]\), noting that \(x^9 - x\) is the difference of two terms. \[ \frac{d}{dx}[(x^9 - x)^9] = 9(x^9 - x)^8 \cdot \frac{d}{dx}[x^9 - x] \] \[ = 9(x^9 - x)^8 \cdot \left( \frac{d}{dx}[x^9] - \frac{d}{dx}[x] \right) \] \[ = 9(x^9 - x)^8 \left( \text{[ ]} \right) \] Therefore, if \(f(x) = (x^9 - x)^9\), then we have the following result. \[ f'(x) = \frac{d}{dx}[(x^9 - x)^9] = \text{[ ]} \]
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Here we have to find differentiation of f(x) 

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