Jan 29, 2013 · According to the extended power rule, we multiply the derivative of the outer function (μ−i)^2 x the derivative of the inner function (xi−μ). The derivative of the outer function brings the 2 …

In other words, the derivative of the sum of two functions is just the sum of their derivatives. We’ll now prove that this is true for any pair of functions. u and v, provided that those functions have derivatives.

Aug 29, 2023 · The sum c 1 f 1 + + c n f n is called a linear combination of functions, and the derivative of that linear combination can be taken term by term, with the constant multiples taken outside the …

Dec 1, 2025 · You often need to apply multiple rules to find the derivative of a function. To find the derivative of f (x) = 3 x 2 + 2 x, you need to apply the sum of derivatives formula and the power rule:

Feb 8, 2025 · Learn the Sum and Difference Rule in differentiation. Understand how to differentiate sums and differences of functions with step-by-step examples.

Sum Rule for finding Derivatives The Sum Rule, also known as the Addition Rule, is a fundamental principle in differentiation used to find the derivative of a sum of two or more functions.

Dec 9, 2025 · The first thing to notice when finding the derivative of this function is that it is the sum of several terms, as shown in color below: ... The Derivative Rule for Sums: The derivative of a sum is …

The derivative of a sum is equal to the total of the derivatives, according to the sum rule for derivatives. When determining the derivative of a sum, we simply add the derivatives together.

Taking the derivative of a function essentially boils down to taking a special limit involving that function. Just as we had a rule that allowed us to find the limit of the sum of functions, we have an analogous …

Free Derivative Sum/Diff Rule Calculator - Solve derivatives using the sum/diff rule method step-by-step