Product Rule
uv’ + vu’
The product rule is a rule for finding the derivative of the product of two functions. It states that the derivative of the product of two functions is equal to the sum of the product of the derivative of the first function and the second function plus the product of the first function and the derivative of the second function.
In mathematical notation, the product rule can be expressed as:
(d/dx)(f(x) * g(x)) = f'(x) * g(x) + f(x) * g'(x)
Where:
– (d/dx) signifies the derivative with respect to x
– f(x) and g(x) are two functions to be multiplied
– f'(x) and g'(x) are the respective derivatives of f(x) and g(x)
The product rule is often used to find the derivatives of functions that can be expressed as the product of two or more functions. It is an important rule in calculus and is used extensively in many applications of mathematics and science, including physics, engineering, and economics.
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