Sums and Differences:1) d/dx [f(x) + g(x)] = ___________________2) d/dx [f(x) – g(x)] = ___________________
1) f'(x) + g'(x)2) f'(x) – g'(x)
1) Using the sum rule of differentiation, the derivative of the sum of two functions f(x) and g(x) with respect to x is equal to the sum of the derivatives of each individual function. Therefore:
d/dx [f(x) + g(x)] = d/dx [f(x)] + d/dx[g(x)]
2) Similarly, using the difference rule of differentiation, the derivative of the difference of two functions f(x) and g(x) with respect to x is equal to the difference between the derivatives of each individual function. Therefore:
d/dx [f(x) – g(x)] = d/dx [f(x)] – d/dx[g(x)]
It is important to note that the sum and difference rules hold true for any two differentiable functions f(x) and g(x).
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