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Sunday, March 2, 2014

Second Derivative Problems - Reciprocal Formula

Category: Differential Calculus, Algebra

"Published in Vacaville, California, USA"

Using the fact that


show that


Solution:

Consider the given equation above


Take the derivative on both sides of the equation with respect to x by quotient formula, we have










Therefore,


Saturday, March 1, 2014

Second Derivative Problems - Quotient Formula

Category: Differential Calculus, Algebra

"Published in Vacaville, California, USA"

Find a formula for


Solution:

The first thing that we have to do is to get the derivative of u/v with respect to x where u and v are functions of x. Apply the derivative by quotient formula, we have 




Take the derivative again of the above equation with respect to x by product formula, we have






 






where:




 

Friday, February 28, 2014

Second Derivative Problems - Product Formula

Category: Differential Calculus, Algebra

"Published in Vacaville, California, USA"

Find a formula for


Solution:

The first thing that we have to do is to get the derivative of uv with respect to x where u and v are functions of x. Apply the derivative by product formula, we have




Take the derivative again of the above equation with respect to x by product formula, we have









where: