d/dx [f(x)g(x)]
f'(x)g(x)+f(x)g'(x)
The product rule of differentiation states that the derivative of the product of 2 functions (f and g) is equal to the first function (f) times the derivative of the second function (g) plus the second function (g) times the derivative of the first function (f).
Applying the product rule to the given function results in:
d/dx [f(x)g(x)] = f(x)(d/dx [g(x)]) + g(x)(d/dx [f(x)])
Therefore, the derivative of f(x)g(x) with respect to x is equal to f(x) times the derivative of g(x) with respect to x plus g(x) times the derivative of f(x) with respect to x.
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