Q. 10 - Calculus

Question

Moreover, the following properties follow from this definition (fill in the blanks or select the correct options):

$\frac{d}{dx}\left(\ln x\right)=\_\_\_ \text{ and }\ln 1=\_\_\_$

Step-by-Step Solution

Answer

The complete expression is,

$$\begin{gathered} \frac{d}{dx}\left(\ln x\right)=\frac{1}{x} \text{ and } \\ \ln 1=0 \end{gathered}$$

Step 1. Given information.

We are given an incomplete statement, 

$\frac{d}{dx}\left(\ln x\right)=\_\_\_ \text{ and }\ln 1=\_\_\_$

Step 2. Completing the statement.

We know that after differentiating the logarithmic function, we get

$$\begin{gathered} \frac{d}{dx}\left(\ln x\right)=\frac{1}{x} \text{ and } \\ \ln 1=0 \end{gathered}$$