To find $y'$ (the derivative of $y$ with respect to $x$), given the function $y = \ln(x^5)$ and the point $(1, 0)$, we'll proceed as follows:

Step 1: Simplify the logarithmic expression

We can use the logarithm power rule: $y = \ln(x^5) = 5\ln(x)$

Step 2: Differentiate the function

Now, differentiate $y = 5\ln(x)$ with respect to $x$: [ y' = \frac{d}{dx}[5\ln(x)] = 5 \cdot \frac{d}{dx}[\ln(x)] ] $y' = 5 \cdot \frac{1}{x} = \frac{5}{x}$

Step 3: Evaluate the derivative at the given point

We are asked to find the derivative at the point $(1, 0)$. Since $x = 1$ at this point: $y' = \frac{5}{1} = 5$

So, the derivative $y'$ at the point $(1, 0)$ is: $\boxed{5}$

Would you like to explore any more details or have additional questions? Here are some related questions to consider:

1. How does the power rule for logarithms work?
2. What is the derivative of a natural logarithm function?
3. How do you interpret the derivative of a logarithmic function?
4. How do you apply the derivative at a specific point?
5. What are the properties of logarithmic functions?

Tip: When differentiating functions involving logarithms, it's often helpful to simplify the logarithmic expression using the logarithm rules before differentiating. This can make the derivative much easier to compute.