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Homesum rule

## Primary tabs

# 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 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 problem: Problem: Show that phi(a^n-1), (where phi is the Euler totient function), is divisible by n for any natural number n and any natural number a >1. by mbhatia

new problem: MSC browser just displays "No articles found. Up to ." by jaimeglz

Mar 26

new correction: Misspelled name by DavidSteinsaltz

Mar 21

new correction: underline-typo by Filipe

Mar 19

new correction: cocycle pro cocyle by pahio

Mar 7

new image: plot W(t) = P(waiting time <= t) (2nd attempt) by robert_dodier

new image: expected waiting time by robert_dodier

new image: plot W(t) = P(waiting time <= t) by robert_dodier

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 problem: Problem: Show that phi(a^n-1), (where phi is the Euler totient function), is divisible by n for any natural number n and any natural number a >1. by mbhatia

new problem: MSC browser just displays "No articles found. Up to ." by jaimeglz

Mar 26

new correction: Misspelled name by DavidSteinsaltz

Mar 21

new correction: underline-typo by Filipe

Mar 19

new correction: cocycle pro cocyle by pahio

Mar 7

new image: plot W(t) = P(waiting time <= t) (2nd attempt) by robert_dodier

new image: expected waiting time by robert_dodier

new image: plot W(t) = P(waiting time <= t) by robert_dodier

## 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