ADVANCED CALCULUS

Total Differentiation

RICHMUND G. ALLORDE

Objectives

2

At the end of the lesson, you should be able to do the following:

Compute the derivative of multivariable functions.

Compute the total derivative of a given multivariable function.

Total Differentiation

3

Total derivative is defined as:

dnn

udy

y

udx

x

udu

...

This swirly-d symbol, ∂, often called "del", is used

to distinguish partial derivatives from ordinary

single-variable derivatives)...,( nyxfu :Given

Total Differentiation

4

dyy

udx

x

udu

This swirly-d symbol, ∂, often called "del", is used

to distinguish partial derivatives from ordinary

single-variable derivatives

23 yxu :Given

223 yxx

u

yxy

u 32

dyyxdxyxdu 2 3 322

Assessment

5

yxyyxf sintan),( :Given

xyx

f 2sec

yxy

fcostan

Find the total derivative of the given function.

dyyxdxxydu costan sec2

dyy

udx

x

udu

Bibliography

6

Bibliography

7

Bibliography

8

Bibliography

9

• https://solitaryroad.com/c353.html

• https://www.youtube.com/watch?v=8PEVJbSbqTg