Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.2 Derivatives And Integrals Involving Logarithmic Functions - Exercises Set 6.2 - Page 425: 34

False

Given $$\frac{d}{d x}\left((\ln x)^{2}\right)=\frac{d}{d x}(2(\ln x))=\frac{2}{x}$$ Since \begin{align*} \frac{d}{d x}\left((\ln x)^{2}\right)&= 2(\ln x) \frac{d}{d x}(\ln x)\\ &=\frac{2\ln x}{x}\neq\frac{2}{x} \end{align*} then the statement false