Sure! The product rule is a formula used in calculus to find the derivative of the product of two functions.
Let's say we have two functions f(x) and g(x). The product rule states that the derivative of the product of f(x) and g(x) is equal to the derivative of f(x) times g(x) plus f(x) times the derivative of g(x).
Mathematically, the product rule can be written as:
(d/dx) [f(x) * g(x)] = f'(x) * g(x) + f(x) * g'(x)
Here, f'(x) represents the derivative of function f(x) with respect to x, and g'(x) represents the derivative of function g(x) with respect to x.
To illustrate this with an example, let's consider the functions f(x) = x^2 and g(x) = x^3. We can find the derivative of their product using the product rule:
(d/dx) [f(x) * g(x)] = (d/dx) [x^2 * x^3]
Applying the product rule:
= (d/dx) [x^2] * x^3 + x^2 * (d/dx) [x^3]
Taking the derivatives individually:
= 2x * x^3 + x^2 * 3x^2
Simplifying:
= 2x^4 + 3x^4
= 5x^4
So, the derivative of the product of f(x) = x^2 and g(x) = x^3 is f'(x) * g(x) + f(x) * g'(x) = 5x^4.
Remember that the product rule is used when taking the derivative of a product of two functions.
Hey boy can u give me an example of a Product Rule and the description of a Product Rule ASAPPPP
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