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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

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

Sep 26

new question: Latent variable by adam_reith

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag

Sep 26

new question: Latent variable by adam_reith

## 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