Questions: Find d/dx(7 ln(x))

Transcript text: Find $\frac{d}{d x}(7 \ln (x))$

Solution

Solution Steps

To find the derivative of the function $7 \ln(x)$ with respect to $x$, we can use the rule for differentiating logarithmic functions. The derivative of $\ln(x)$ is $\frac{1}{x}$. Therefore, the derivative of $7 \ln(x)$ is $7$ times the derivative of $\ln(x)$.

Step 1: Identify the Function

The function given is $7 \ln(x)$. We need to find its derivative with respect to $x$.

Step 2: Apply the Derivative Rule for Logarithmic Functions

The derivative of $\ln(x)$ is $\frac{1}{x}$. Therefore, the derivative of $7 \ln(x)$ is calculated by multiplying 7 by the derivative of $\ln(x)$.

Step 3: Calculate the Derivative

Using the rule from Step 2, the derivative of $7 \ln(x)$ is: \[ \frac{d}{dx}(7 \ln(x)) = 7 \cdot \frac{1}{x} = \frac{7}{x} \]