f'(x) – g'(x)
derivative of the difference between two functions
The expression f'(x) – g'(x) represents the difference between the derivative of f(x) and the derivative of g(x) with respect to the independent variable x.
To evaluate this expression, we first need to find the derivative of both f(x) and g(x) separately, using the rules of differentiation.
Let’s assume that f(x) and g(x) are two functions of x. Then, the derivative of f(x) is denoted as f'(x) and can be found using the power rule of differentiation, chain rule, or other differentiation rules, depending on the function. Similarly, the derivative of g(x) is denoted as g'(x) and can also be found using the rules of differentiation.
Once we have f'(x) and g'(x), we can simply subtract the two derivatives to get the expression f'(x) – g'(x). This expression represents the rate of change of f(x) minus the rate of change of g(x) at any given point x. It can give us information about the relative growth rates or trends of the two functions, which can be useful in many applications.
In summary, f'(x) – g'(x) represents the difference between the derivatives of two functions f(x) and g(x) with respect to x. We can find this expression by first finding the individual derivatives of f(x) and g(x), and then subtracting them.
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