Nth Derivative of Transcedental Functions Formula Part 1

TL;DR

This video explains how to find the nth derivative of algebraic functions using a step-by-step approach.

Transcript

hi friends so in this video we are gonna see nth derivative of some more functions let's take an example if y is a x plus b raised to minus m then what is the nth derivative of this now to find the nth derivative we are gonna follow one approach that is we will find the first derivative that is y one second derivative y two then third derivative y ... Read More

Key Insights

• 💭 The nth derivative of an algebraic function can be found by using the first three derivatives to identify the pattern and derive a general formula.
• 😒 The derived formula for the nth derivative involves the use of factorials, exponents, and coefficients.
• 💭 The formula for the nth derivative can be applied to find higher-order derivatives of different algebraic functions.
• 💭 The derived formula simplifies the process of finding the nth derivative by providing a direct calculation method.
• 💭 Substituting different values for the parameters in the derived formula can yield specific formulas for the nth derivative of specific algebraic functions.
• 🤨 The video also provides a corollary for finding the nth derivative of y = ax + b raised to -1.
• 💭 The formulas for the nth derivative can be used to solve complex mathematical problems, particularly in calculus and differential equations.

Questions & Answers

Q: How do you find the nth derivative of an algebraic function?

To find the nth derivative, you can use the first three derivatives to predict the pattern and apply the derived formula for the nth derivative.

Q: What is the formula for the nth derivative of a function?

The formula for the nth derivative of a function y = ax + b raised to -m is (-1)^n * m * (m+1) * (m+2) * ... * (m+n-1) * a^n / (12...*(m-1)) * (ax + b)^(m+n).

Q: How do you find the nth derivative of y = ax + b raised to -1?

The formula for the nth derivative of y = ax + b raised to -1 is (-1)^n * n! * a^n / (ax + b)^(n+1), where n is the desired derivative order.

Q: Why are the derived formulas useful?

The derived formulas for the nth derivative of algebraic functions provide a systematic approach to finding higher-order derivatives, which can be helpful in solving various mathematical problems and applications.

Summary & Key Takeaways

• The video explains how to find the nth derivative of a function using the first three derivatives to predict the pattern.

• The formula for finding the nth derivative of a function is derived and explained in detail.

• A corollary is given for finding the nth derivative of the function y = ax + b raised to -1.