Differentiation Formulas
The derivative of standard functions can be found by the formulas. We will learn the Differentiation formulas of the following functions:
- Algebraic Function
- Exponential Function
- Logarithmic Function
- Trigonometric Function
Derivative of Algebraic Functions
y = f(x) | dy/dx |
---|---|
[Tex]\frac{d}{dx}(x^n)[/Tex] | [Tex]nx^{n-1}[/Tex] |
[Tex] \frac{d}{dx} (\frac{1}{x})[/Tex] | [Tex]-\frac{1}{x^2}[/Tex] |
[Tex]\frac{d}{dx} (√x) [/Tex] | [Tex]\frac{1}{2√x}[/Tex] |
Derivative of Exponential Functions
y = f(x) | dy/dx |
---|---|
[Tex]\frac{d}{dx} (e^x)[/Tex] | ex |
[Tex] \frac{d}{dx} (a^x) [/Tex] | ax logea |
Derivative of Logarithmic Functions
y = f(x) | dy/dx |
---|---|
[Tex] \frac{d}{dx} ( log_ex) [/Tex] | 1/x |
[Tex]\frac{d}{dx} ( log_ax)[/Tex] | [Tex]\frac{1}{x log_ea}[/Tex] |
Learn More: logarithmic differentiation
Derivative of Trigonometric Functions
y = f(x) | dy/dx |
---|---|
[Tex]\frac{d}{dx} (sin x) [/Tex] | cos x |
[Tex]\frac{d}{dx}( cos x) [/Tex] | -sin x |
[Tex]\frac{d}{dx} ( tan x) [/Tex] | sec2x |
[Tex]\frac{d}{dx} (cot x)[/Tex] | -cosec2x |
[Tex]\frac{d}{dx} (sec x) [/Tex] | sec x.tan x |
[Tex]\frac{d}{dx} (cosec x) [/Tex] | -cosec x.cot x |
The above formulas are used when the functions are present alone or when multiplied by a scalar number but when two functions are in product form or quotient form then we can’t simply differentiate each function separately but we need to follow some rules, particularly for product and quotient case. Hence, we will look at differentiation by parts.
Differentiation and Integration Formula
Differentiation and Integration are two mathematical operations used to find change in a function or a quantity with respect to another quantity instantaneously and over a period, respectively. Differentiation is an instantaneous rate of change and it breaks down the function for that instant with respect to a particular quantity while Integration is the average rate of change that causes the summation of continuous data of a function over the given period or range. Both are inverse of each other.
In this article, we will learn about what is differentiation, what is integration, and the formulas related to Differentiation and Integration.
Table of Content
- What is Differentiation?
- How to Differentiate a Function
- Differentiation Formulas
- Derivative of Algebraic Functions
- Derivative of Exponential Functions
- Derivative of Logarithmic Functions
- Derivative of Trigonometric Functions
- Differentiation by Parts
- What is Integration?
- How to Integrate Function
- Integration Formulas
- Integration of Algebraic Functions
- Integration of Exponential Functions
- Integration of Trigonometric Functions
- Integration By Parts
- Area Under the Curve
- Differentiation and Integration Formulas
- Properties of Differentiation and Integration
- Difference between Differentiation and Integration
- Solved Examples of Differentiation and Integration Formula
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