$\dfrac{d}{dx}{\, (x^{\displaystyle n})}$ $\,=\,$ $n.x^{\, \displaystyle n\small -1}$

The derivative of an exponential term, which contains a variable as base and a constant as power, is called the constant power derivative rule.

$x$ and $n$ are literals and they represent a variable and a constant. They form an exponential term $x^n$. The derivative of $x$ is raised to the power $n$ is written in mathematical form as follows.

$\dfrac{d}{dx}{\, (x^{\displaystyle n})}$

The differentiation of $n$-th power of $x$ with respect to $x$ is equal to the product of $n$ and $x$ raised to the power of $n$ minus one.

$\dfrac{d}{dx}{\, (x^{\displaystyle n})}$ $\,=\,$ $n.x^{\, \displaystyle n\small -1}$

The derivative of a constant power rule can be written in terms of any variable and constant.

$(1) \,\,\,\,\,\,$ $\dfrac{d}{dh}{\, (h^{\displaystyle c})}$ $\,=\,$ $c.h^{\, \displaystyle c\small -1}$

$(2) \,\,\,\,\,\,$ $\dfrac{d}{dl}{\, (l^{\displaystyle m})}$ $\,=\,$ $m.l^{\, \displaystyle m\small -1}$

$(3) \,\,\,\,\,\,$ $\dfrac{d}{dy}{\, (y^{\displaystyle p})}$ $\,=\,$ $p.y^{\, \displaystyle p\small -1}$

Learn how to prove the derivative of a constant power rule in differential calculus by first principle.

Latest Math Topics

Apr 18, 2022

Apr 14, 2022

Apr 05, 2022

Mar 18, 2022

Mar 05, 2022

Latest Math Problems

Apr 06, 2022

Mar 22, 2022

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

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

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

Copyright © 2012 - 2021 Math Doubts, All Rights Reserved