d/dx [f(x) ± g(x)]
f'(x) ± g'(x)
The derivative of the sum or difference of two functions f(x) and g(x) is equal to the sum or difference of their individual derivatives. Therefore, the derivative of [f(x) ± g(x)] with respect to x is:
d/dx [f(x) ± g(x)] = d/dx [f(x)] ± d/dx [g(x)]
In other words, we can differentiate each function separately and then add or subtract their derivatives.
For example, if we have two functions f(x) = x^2 and g(x) = 3x, then:
d/dx [f(x) + g(x)] = d/dx [x^2 + 3x]
= d/dx [x^2] + d/dx [3x]
= 2x + 3
Similarly, the derivative of [f(x) – g(x)] would be:
d/dx [f(x) – g(x)] = d/dx [f(x)] – d/dx [g(x)]
= d/dx [x^2] – d/dx [3x]
= 2x – 3
So, the answer to the question d/dx [f(x) ± g(x)] is d/dx [f(x)] ± d/dx [g(x)].
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