f'[g(x)]×g'(x) is what derivative rule?
The expression f'[g(x)] × g'(x) represents the product rule of differentiation
The expression f'[g(x)] × g'(x) represents the product rule of differentiation.
In calculus, the product rule is a method used to find the derivative of a product of two functions. It states that if we have two functions being multiplied together, say f(x) and g(x), their derivative can be found by taking the derivative of the first function, f'(x), and multiplying it by the second function, g(x), and then adding it to the derivative of the second function, g'(x), multiplied by the first function, f(x). Mathematically, this can be expressed as:
(d/dx) [f(x) * g(x)] = f'(x) * g(x) + f(x) * g'(x)
Going back to the given expression f'[g(x)] × g'(x), we can see that it matches the format of the product rule. Here, f(x) is replaced by f'[g(x)] and g(x) is replaced by g'(x). Thus, using the product rule, the derivative of f'[g(x)] × g'(x) can be found as:
(d/dx) [f'[g(x)] × g'(x)] = f”[g(x)] × g'(x) + f'[g(x)] × g”(x)
So, the derivative rule for the expression f'[g(x)] × g'(x) is the product rule.
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