There are some standard results with algebraic functions and they are used as formulas in differential calculus to find the differentiation of algebraic functions.

The derivative of any constant with respect to a variable is equal to zero.

$\dfrac{d}{dx}{\, (c)} \,=\, 0$

The derivative of a variable with respect to same variable is equal to one.

$\dfrac{d}{dx}{\, (x)} \,=\, 1$

The derivative of square root of a variable with respect to same variable is equal to the quotient of one by two times the square root of the variable.

$\dfrac{d}{dx}{\, \sqrt{x}} \,=\, \dfrac{1}{2\sqrt{x}}$

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

$(2) \,\,\,\,\,$ $\dfrac{d}{dx}{\, e^x} \,=\, e^x$

$(3) \,\,\,\,\,$ $\dfrac{d}{dx}{\, a^x} \,=\, a^x\log{a}$

$\dfrac{d}{dx}{\, \log_{e}{(x)}} \,=\, \dfrac{1}{x}$

Latest Math Topics

Nov 03, 2022

Jul 24, 2022

Jul 15, 2022

Latest Math Problems

Nov 25, 2022

Nov 02, 2022

Oct 26, 2022

Oct 24, 2022

Sep 30, 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 - 2022 Math Doubts, All Rights Reserved