# What is the Sum Rule for derivatives?

The sum rule for derivatives states that the derivative of a sum is equal to the sum of the derivatives.

In symbols, this means that for

For an example, consider a cubic function:

Note that A, B, C, and D are all constants. Now we will make use of three other basic properties, two of which are illustrated together below, without proof.

Using all four of these properties, we can find the derivative of our cubic expression.

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The Sum Rule for derivatives states that the derivative of the sum of two functions is equal to the sum of their derivatives. In mathematical notation, if ( f(x) ) and ( g(x) ) are two functions, then the derivative of their sum, denoted ( (f(x) + g(x))' ) or ( \frac{d}{dx}(f(x) + g(x)) ), is equal to the sum of their derivatives individually, i.e., ( f'(x) + g'(x) ). Mathematically, it can be expressed as:

[ \frac{d}{dx}(f(x) + g(x)) = f'(x) + g'(x) ]

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The Sum Rule for derivatives states that if ( f(x) ) and ( g(x) ) are differentiable functions, then the derivative of their sum is equal to the sum of their derivatives:

[ \frac{d}{dx}(f(x) + g(x)) = \frac{d}{dx}f(x) + \frac{d}{dx}g(x) ]

In other words, the derivative of the sum of two functions is equal to the sum of the derivatives of the individual functions. This rule holds true for any real-valued functions ( f(x) ) and ( g(x) ).

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