# Chapter 6 - Applications of Integration - 6.8 Logarithmic and Exponential - 6.8 Exercises: 9

$$\frac{{\cos \left( {\ln x} \right)}}{x}$$

#### Work Step by Step

\eqalign{ & \frac{d}{{dx}}\left( {\sin \left( {\ln x} \right)} \right) \cr & {\text{use the rule }}\frac{d}{{dx}}\left( {\sin u} \right) = \cos u\frac{{du}}{{dx}},{\text{ letting }}u = \ln x \cr & = \cos \left( {\ln x} \right)\frac{d}{{dx}}\left( {\ln x} \right) \cr & = \cos \left( {\ln x} \right)\left( {\frac{1}{x}} \right) \cr & {\text{multiply}} \cr & = \frac{{\cos \left( {\ln x} \right)}}{x} \cr}

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