# Chapter 7 - Exponential Functions - 7.3 Logarithms and Their Derivatives - Exercises - Page 343: 32

$\frac{5}{x}$

#### Work Step by Step

$y= \ln (x^{5})$ Put $t= x^{5}$ Then, $y=\ln t$ According to the chain rule, $\frac{dy}{dx}=\frac{dy}{dt}\cdot\frac{dt}{dx}=\frac{1}{t}\times5x^{4}$ $=\frac{5x^{4}}{x^{5}}=\frac{5}{x}$

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