Understanding the Product Rule of Differentiation for f(x)g(x) Derivatives

d/dx[f(x)g(x)]

The expression d/dx[f(x)g(x)] represents the derivative of the function f(x)g(x) with respect to x

The expression d/dx[f(x)g(x)] represents the derivative of the function f(x)g(x) with respect to x. To find this derivative, we can use the product rule of differentiation.

Product Rule:
If we have two functions u(x) and v(x), the derivative of their product is given by:
d/dx(u(x)v(x)) = [u'(x)v(x)] + [u(x)v'(x)],

where u'(x) represents the derivative of u(x) with respect to x, and v'(x) represents the derivative of v(x) with respect to x.

Applying the product rule to the function f(x)g(x), we get:
d/dx[f(x)g(x)] = [f'(x)g(x)] + [f(x)g'(x)],

where f'(x) represents the derivative of f(x) with respect to x, and g'(x) represents the derivative of g(x) with respect to x.

In summary, to find the derivative of f(x)g(x) with respect to x, we need to find the derivative of both f(x) and g(x), and then use the product rule to combine those derivatives.

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