d/dx [f(x)g(x)]
f(x)g'(x) + g(x)f'(x)
To find the derivative of the product of two functions f(x) and g(x) with respect to x, we use the product rule.
Product Rule:
(d/dx)[f(x)g(x)] = f(x) d/dx[g(x)] + g(x) d/dx[f(x)]
So, taking the derivative of the product f(x)g(x), we get:
(d/dx)[f(x)g(x)] = f(x) d/dx[g(x)] + g(x) d/dx[f(x)]
Therefore, the derivative of the product f(x)g(x) with respect to x is the first function f(x) times the derivative of the second function g(x), plus the second function g(x) times the derivative of the first function f(x).
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