d/dx[f(x)g(x)] (product rule)
To find the derivative of the product of two functions f(x) and g(x) with respect to x, we can use the product rule
To find the derivative of the product of two functions f(x) and g(x) with respect to x, we can use the product rule. The product rule states that the derivative of the product of two functions is equal to the derivative of the first function times the second function, plus the first function times the derivative of the second function. Mathematically,
d/dx[f(x)g(x)] = f'(x)g(x) + f(x)g'(x)
Let’s break down the steps to find the derivative using the product rule:
Step 1: Differentiate the first function f(x) with respect to x, denoted as f'(x).
Step 2: Keep the second function g(x) as it is.
Step 3: Add the product of f'(x) and g(x) to the product of f(x) and g'(x).
So, the derivative of f(x)g(x) is f'(x)g(x) + f(x)g'(x).
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