Product Rule: d/dx [ f(x) * g(x) ]
The product rule is a rule in calculus used to find the derivative of a function that is the product of two other functions
The product rule is a rule in calculus used to find the derivative of a function that is the product of two other functions. It is expressed as:
d/dx [ f(x) * g(x) ] = f(x) * g'(x) + g(x) * f'(x)
where f(x) is the first function, g(x) is the second function, and f'(x) and g'(x) represent their respective derivatives.
To apply the product rule, follow these steps:
1. Identify the first function f(x) and the second function g(x).
2. Find the derivative of the first function f'(x).
3. Find the derivative of the second function g'(x).
4. Multiply the first function f(x) by the derivative of the second function g'(x).
5. Multiply the second function g(x) by the derivative of the first function f'(x).
6. Add the two results obtained in steps 4 and 5. This sum represents the derivative of the product of the two functions.
Let’s use the product rule to find the derivative of f(x) * g(x):
d/dx [ f(x) * g(x) ] = f(x) * g'(x) + g(x) * f'(x)
This formula shows that the derivative of the product is equal to the first function times the derivative of the second function, plus the second function times the derivative of the first function.
Remember, to find the derivative of each function, you may need to use additional rules such as the power rule or the chain rule.
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