Product rule of f(x)g(x)
f'(x)g(x)+g'(x)f(x)
The product rule is a formula used in calculus to find the derivative of a function that is the product of two other functions. The product rule is stated as follows:
Let f(x) and g(x) be two functions of x. Then, the derivative of their product f(x)g(x) is given by:
(fg)'(x) = f'(x)g(x) + f(x)g'(x)
This formula implies that when taking the derivative of a product of two functions, we first take the derivative of the first function times the second function, followed by the product of the first function and the derivative of the second function. In other words, we differentiate f(x) and g(x) separately and then add them together.
In notation form, we can represent the product rule as:
(d/dx)[f(x)g(x)] = f'(x)g(x) + f(x)g'(x)
where f'(x) and g'(x) represent the derivative of f(x) and g(x) with respect to x, respectively.
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