# Derivative properties

There are six properties in differential calculus and they are used as formulas in differentiation. So, learn the following list of properties of derivatives with proofs and also example problems with solutions to learn how to use them in differentiating the functions.

### Operations

$(1).\,\,\,$ $\dfrac{d}{dx}{\Big(f{(x)}+g{(x)}\Big)}$ $\,=\,$ $\dfrac{d}{dx}{f{(x)}}$ $+$ $\dfrac{d}{dx}{g{(x)}}$

$(2).\,\,\,$ $\dfrac{d}{dx}{\Big(f{(x)}-g{(x)}\Big)}$ $\,=\,$ $\dfrac{d}{dx}{f{(x)}}$ $-$ $\dfrac{d}{dx}{g{(x)}}$

$(3).\,\,\,$ $\dfrac{d}{dx}{\Big(f(x) \times g(x)\Big)}$ $\,=\,$ $f(x)\dfrac{d}{dx}{g(x)}$ $+$ $g(x)\dfrac{d}{dx}{f(x)}$

$(4).\,\,\,$ $\dfrac{d}{dx}{\Bigg(\dfrac{f(x)}{g(x)}\Bigg)}$ $\,=\,$ $\dfrac{g(x)\dfrac{d}{dx}{f(x)}-f(x)\dfrac{d}{dx}{g(x)}}{g{(x)}^2}$

### Reciprocal rule

$\dfrac{d}{dx}{\bigg(\dfrac{1}{f(x)}\bigg)}$ $\,=\,$ $-\,\dfrac{1}{\Big(f(x)\Big)^2} \times \dfrac{d}{dx}{\Big(f(x)\Big)}$

### Constant multiple rule

$\dfrac{d}{dx}{\, \Big(k.f(x)\Big)} \,=\, k \times \dfrac{d}{dx}{\, f(x)}$

### Chain rule

$\dfrac{d}{dx} {f\big({g(x)}\big)} \,=\, {f’\big({g(x)}\big)}.{g'{(x)}}$

#### Formulas

List of the differentiation formulas with proofs and example problems to learn how to use some standard results as formulas in differentiating the functions.

Latest Math Problems

A best free mathematics education website for students, teachers and researchers.

###### Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

###### Maths Problems

Learn how to solve the maths problems in different methods with understandable steps.

Learn solutions

###### Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.