d/dx f(x)g(x)
f(x)g'(x) + g(x)f'(x)
To differentiate the product of two functions f(x) and g(x) with respect to x, we can use the product rule of differentiation which is given by:
d/dx [f(x)g(x)] = f(x)g'(x) + g(x)f'(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.
Therefore, the derivative of f(x)g(x) with respect to x is:
d/dx [f(x)g(x)] = f(x)g'(x) + g(x)f'(x)
This formula tells us that we first take the product of f(x) and the derivative of g(x) with respect to x (g'(x)), and then we add this result to the product of g(x) and the derivative of f(x) with respect to x (f'(x)).
Note that the order in which we multiply the functions f(x) and g(x) does not matter because multiplication is commutative. Additionally, if either f(x) or g(x) is a constant function, then its derivative with respect to x will be zero.
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