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

The derivative of difference of functions is equal to the difference of their derivatives, is called the difference rule of differentiation.

The derivative of difference of any two functions is often required to calculate in differential calculus in some cases. Actually, it is impossible to find the derivative of two different functions directly. However, it can be calculated from its equivalent operation by calculating the difference of their derivatives.

$f{(x)}$ and $g{(x)}$ are two functions in terms of a variable $x$ and the derivative of difference of them can be calculated by the difference of their derivatives.

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

The difference rule of derivatives is also written in two different ways in differential calculus popularly.

$(1) \,\,\,$ $\dfrac{d}{dx}{\, (u-v)}$ $\,=\,$ $\dfrac{du}{dx}$ $-$ $\dfrac{dv}{dx}$

$(2) \,\,\,$ ${d}{\, (u-v)}$ $\,=\,$ $du$ $-$ $dv$

Learn how to derive the difference rule of derivatives by first principle in differential calculus.

Latest Math Topics

Dec 13, 2023

Jul 20, 2023

Jun 26, 2023

Latest Math Problems

Jan 30, 2024

Oct 15, 2023

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved