Derivative of the Summation of Two Functions: Applying the Sum Rule of Differentiation

derivative of the summation of two functions

f'(x) + g'(x)

The derivative of the summation of two functions can be found by taking the derivative of each of the individual functions and then adding them together.

Let’s say we have two functions, f(x) and g(x).

The summation of these two functions can be represented as (f(x) + g(x)).

To find the derivative of this summation, we will apply the derivative operation to each function separately.

Taking the derivative of f(x) with respect to x will give us f'(x), and taking the derivative of g(x) with respect to x will give us g'(x).

Now, we can apply the sum rule of differentiation, which states that the derivative of the sum of two functions is equal to the sum of the derivatives of those individual functions.

So, the derivative of the summation (f(x) + g(x)) will be (f'(x) + g'(x)).

In summary, to find the derivative of the summation of two functions, we simply take the derivative of each function individually and then add them together.

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