The given equation is:

$y = \frac{1}{(1 - 3x)^5}$

We are asked to find the gradient (or slope) of the curve at $x = 1$. This means we need to compute the derivative of $y$ with respect to $x$ and evaluate it at $x = 1$.

Steps:

1. Differentiate $y = \frac{1}{(1 - 3x)^5}$ with respect to $x$, using the chain rule.
2. Plug in $x = 1$ into the derivative to find the gradient at that point.

I'll compute this now.The derivative of $y = \frac{1}{(1 - 3x)^5}$ with respect to $x$ is:

$\frac{dy}{dx} = \frac{15}{(1 - 3x)^6}$

At $x = 1$, the gradient of the curve is:

$\frac{dy}{dx} \bigg|_{x=1} = \frac{15}{64}$

Thus, the gradient of the curve at $x = 1$ is $\frac{15}{64}$.

Would you like more details on any step?

Here are five related questions:

1. How do you apply the chain rule in this differentiation?
2. Why is it important to simplify the derivative before evaluation?
3. How do you interpret the gradient of a curve geometrically?
4. What is the significance of the power rule in this context?
5. How does the steepness of the curve change as $x$ increases?

Tip: Always check if a function has any undefined points before evaluating at specific values to avoid errors in calculus.