If u, v and w are functions of x, then show that `d/(dx)(u.v.w)=(d u)/(dx)v.w+u.(d v)/(dx).w+u.v(d w)/(dx)` in two ways - first by repeated application of product rule, second by logarithmic differentiation.

Explanation

To show that \(\frac{d}{dx}(uvw) = \frac{du}{dx}vw + u\frac{dv}{dx}w + uv\frac{dw}{dx}\), we will approach this in two ways: using the product rule and using logarithmic differentiation.

### Method 1: Repeated Application of the Product Rule

1. **Define the function**:
Let \( f(x) = u(x) \cdot v(x) \cdot w(x) \).

2. **Apply the product rule**:
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