 output.to from Sideway
Draft for Information Only

# Content

```Successive Differentiation  nᵗʰ Derivative of Function ```

# Successive Differentiation

In general, the differentiation of a function can be differentiated succesively to obtain Higher Order Derivatives. Let function y=f(x) be a function of x. Then the result of differentiating y with respect to x is defined as the derivative or the first derivative of y with respect to x and is denoted as Then the result of differentiating ƒ(x) with respect to x is defined the second differential derivative of y with respect to x and is denoted as Similarly, the result of differentiating ƒ(x) with respect to x is defined the third differential derivative of y with respect to x and is denoted as By continuing the differentiation process, the result of differentiating ƒ(x) n times with respect to x successively is defined the nth differential derivative of y with respect to x and is denoted as The second, third, fourth, ..., nth derivatives are called higher order derivatives.

## nᵗʰ Derivative of Function

1. nth Derivative of General Polynomial Function Proof: 2. nth Derivative of General Natural Exponential Function Proof: 3. nth Derivative of General Exponential Function Proof: 4. nth Derivative of General Natural Logarithmic Function Proof: 5. nth Derivative of General Sine Function Proof: 6. nth Derivative of General Cosine Function Proof: 7. nth Derivative of Product of General Functions Proof: 8. nth Derivative of Product of General Functions Proof: 9. nth Derivative of Product of Functions (Leibnitz's Theorem) Proof: ID: 130700029 Last Updated: 7/15/2013 Revision: 0 Ref: References

1. S. James, 1999, Calculus
2. B. Joseph, 1978, University Mathematics: A Textbook for Students of Science &amp; Engineering  Home 5

Management

HBR 3

Information

Recreation

Culture

Chinese 1097

English 339

Reference 79 Computer

Hardware 224 Software

Application 213

Latex 52 Manim 204

KB 1

Numeric 19

Programming

Web 289

Unicode 504

HTML 66

CSS 65

SVG 46

ASP.NET 270

OS 429

Python 72

Knowledge

Mathematics

Algebra 84

Geometry 33 Calculus 67

Engineering

Mechanical

Rigid Bodies

Statics 92

Dynamics 37

Control

Natural Sciences

Electric 27