Chapter 3 - Derivatives - 3.9 Derivatives of Logarithmic and Exponential Functions - 3.9 Exercises - Page 211: 9

$\frac{1}{x}$

y= $\ln 7x$ Put 7x= u Then, y= In u According to the chain rule, $\frac{dy}{dx}= \frac{dy}{du}.\frac{du}{dx}$ That is, $\frac{dy}{dx}= \frac{1}{u}.7$= 7/u Substituting the value of u, We have $\frac{dy}{dx}= \frac{7}{7x}= \frac{1}{x}$