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Homesum rule

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# sum rule

$\frac{\mathrm{d}}{\mathrm{d}x}\left[f(x)+g(x)\right]=f^{{\prime}}(x)+g^{{% \prime}}(x)$ |

# Proof

See the proof of the sum rule.

# Examples

$\displaystyle\frac{\mathrm{d}}{\mathrm{d}x}(x+1)$ | $\displaystyle=$ | $\displaystyle\frac{\mathrm{d}}{\mathrm{d}x}x+\frac{\mathrm{d}}{\mathrm{d}x}1=1$ | ||

$\displaystyle\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-3x+2)$ | $\displaystyle=$ | $\displaystyle\frac{\mathrm{d}}{\mathrm{d}x}x^{2}+\frac{\mathrm{d}}{\mathrm{d}x% }(-3x)+\frac{\mathrm{d}}{\mathrm{d}x}(2)=2x-3$ | ||

$\displaystyle\frac{\mathrm{d}}{\mathrm{d}x}(\sin x+\cos x)$ | $\displaystyle=$ | $\displaystyle\frac{\mathrm{d}}{\mathrm{d}x}\sin x+\frac{\mathrm{d}}{\mathrm{d}% x}\cos x=\cos x-\sin x$ |

Related:

Derivative,ProductRule, FixedPointsOfNormalFunctions

Type of Math Object:

Theorem

Major Section:

Reference

Groups audience:

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## Recent Activity

Apr 22

new question: Prove that for any sets A, B, and C, An(BUC)=(AnB)U(AnC) by St_Louis

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new image: information-theoretic-distributed-measurement-dds.png by rspuzio

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Apr 15

new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia

new question: Prove that for any sets A, B, and C, An(BUC)=(AnB)U(AnC) by St_Louis

Apr 20

new image: information-theoretic-distributed-measurement-dds.png by rspuzio

new image: information-theoretic-distributed-measurement-4.2 by rspuzio

new image: information-theoretic-distributed-measurement-4.1 by rspuzio

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new image: information-theoretic-distributed-measurement-3.1 by rspuzio

new image: information-theoretic-distributed-measurement-2.1 by rspuzio

Apr 19

new collection: On the Information-Theoretic Structure of Distributed Measurements by rspuzio

Apr 15

new question: Prove a formula is part of the Gentzen System by LadyAnne

Mar 30

new question: A problem about Euler's totient function by mbhatia

## Comments

## sequences

how about proving sum and product rules for general sequences tending to a limit, first. since you are effectively using those to prove sume and product rules for differentiability