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

The derivative of product of a constant and a function is equal to the product of constant and the derivative of the function. This property of differentiation is called the constant multiple rule of derivatives.

Let’s take $x$ is a variable, $k$ is a constant and $f(x)$ is a function in terms of $x$. If the constant $k$ is multiplied by the function $f(x)$, then the product of them is $k.f(x)$, which is called as the constant multiple function.

The derivative of the constant multiple function with respect to $x$ is written in mathematical form as follows.

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

The differentiation of the constant multiple function with respect to $x$ is equal to the product of the constant $k$ and the derivative of the function $f(x)$.

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

This property is called the constant multiple rule of differentiation and it is used as a formula in differential calculus.

Look at the following examples to understand the use of the constant multiple rule in differential calculus.

$(1) \,\,\,$ $\dfrac{d}{dx}{\, \Big(6x^2\Big)} \,=\, 6 \times \dfrac{d}{dx}{\, x^2}$

$(2) \,\,\,$ $\dfrac{d}{dy}{\, \Bigg(\dfrac{\log_{e}{y}}{4}\Bigg)} \,=\, \dfrac{1}{4} \times \dfrac{d}{dy}{\, \log_{e}{y}}$

$(3) \,\,\,$ $\dfrac{d}{dz}{\, \Big(-0.7\sin{3z}\Big)} \,=\, -0.7 \times \dfrac{d}{dx}{\, \sin{3z}}$

Learn how to derive the constant multiple rule in differential calculus.

Latest Math Topics

Aug 31, 2024

Aug 07, 2024

Jul 24, 2024

Dec 13, 2023

Latest Math Problems

Sep 04, 2024

Jan 30, 2024

Oct 15, 2023

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved