Difference Rule
Function – f – gDerivative – f’ − g’
The difference rule or subtracting rule is a differentiation technique used to find the derivative of two functions that are subtracted from each other.
The rule states that if we have two functions, say f(x) and g(x), then the derivative of their difference is equal to the difference of their derivatives. That is,
d/dx [f(x) – g(x)] = d/dx [f(x)] – d/dx [g(x)]
or
(f(x) – g(x))’ = f'(x) – g'(x)
In other words, to differentiate the difference of two functions, we can differentiate each function separately and then subtract the two derivatives.
For example, suppose we have the function h(x) = x^3 – 2x^2 + 3x – 5. We can use the difference rule to find the derivative of h(x) as follows:
h'(x) = [d/dx (x^3)] – [d/dx (2x^2)] + [d/dx (3x)] – [d/dx (5)]
Using the power rule of differentiation, we get:
h'(x) = 3x^2 – 4x + 3
So the derivative of h(x) is 3x^2 – 4x + 3.
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