To differentiate the product of two functions, f(x).g(x), we use the product rule.

$\frac{d}{dx}[f(x).g(x)] = f'(x).g(x) + f(x).g'(x)$

The derivative of a product is the derivative of the first times the second plus the first times the derivative of the second.

The formula is clearer if we write the functions simply as f and g.

$\frac{d}{dx}(f.g) = f'.g + f.g'$
Step 1: Write the given function in which the product rule has to be applied.
Step 2: Apply the product rule to find the derivative.
Step 3: Simplify to obtain the derivative of the each function.