## 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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