Chain Rule 7F4370

1. **Stating the problem:** We are given a function $y$ that depends on $u$, which in turn depends on $x$. We want to find the derivative $\frac{dy}{dx}$ using the chain rule. 2. **Formula used:** The chain rule states that if $y = f(u)$ and $u = g(x)$, then $$\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$$ 3. **Explanation:** This means to find the rate of change of $y$ with respect to $x$, we multiply the rate of change of $y$ with respect to $u$ by the rate of change of $u$ with respect to $x$. 4. **Intermediate work:** Suppose $y = f(u)$ and $u = g(x)$, then $$\frac{dy}{dx} = \frac{dy}{du} \times \frac{du}{dx}$$ No further simplification is possible without specific functions. 5. **Summary:** The derivative $\frac{dy}{dx}$ is found by multiplying $\frac{dy}{du}$ and $\frac{du}{dx}$ according to the chain rule.