d/dx[f(x) + g(x)]=
f'(x) + g'(x)
The derivative of the sum of two functions f(x) and g(x) with respect to x is the sum of the individual derivatives, i.e.,
d/dx [f(x) + g(x)] = d/dx [f(x)] + d/dx [g(x)]
In other words, we can find the derivative of f(x) + g(x) by differentiating each of the functions separately and adding them together.
For example, let’s suppose we have two functions f(x) = 3x^2 and g(x) = 2x^3 – 4x. Then, the derivative of f(x) with respect to x is:
d/dx [f(x)] = d/dx [3x^2] = 6x
And the derivative of g(x) with respect to x is:
d/dx [g(x)] = d/dx [2x^3 – 4x] = 6x^2 – 4
Therefore, the derivative of the sum of these two functions is:
d/dx [f(x) + g(x)] = d/dx [3x^2 + (2x^3 – 4x)]
= d/dx [3x^2] + d/dx [2x^3 – 4x]
= 6x + (6x^2 – 4)
= 6x^2 + 6x – 4
Hence, the derivative of f(x) + g(x) is 6x^2 + 6x – 4.
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