Inside function and outside function, Mathematics

"Inside function" and "outside function : Generally we don't actually do all the composition stuff in using the Chain Rule. That can get little complexes and actually obscures the fact that there is a quick & easy way of remembering the chain rule which doesn't need us to think in terms of function composition.

Let's take the following function

1547_inside function.png

This function contain an "inside function" & an "outside function". The outside function is square root/ the exponent of  ½ based on how you desire to think of it and the inside function is the stuff that we're taking the square root of or raising to the  1 , again based o how you desire to look at it.

Then the derivative is,

1384_outside function2.png

Generally it is how we think of the chain rule.  We recognize the "inside function" & the "outside function". Then we differentiate the outside function leaving the inside function alone & multiply all of this by the derivative of the inside function.  General form of this is following,

370_inside function3.png

We can always identify the "outside function" in the examples below by asking ourselves how we would evaluate the function.  In the R(z) case if we were to ask ourselves what R(2)

is we would primary evaluate the stuff under the radical and then finally take the square root of thisresult. The square root is the last operation that we perform in the evaluation and this is also the outside function. The outside function will for all time be the last operation you would perform if you were going to evaluate the function.

Posted Date: 4/12/2013 3:50:53 AM | Location : United States







Related Discussions:- Inside function and outside function, Assignment Help, Ask Question on Inside function and outside function, Get Answer, Expert's Help, Inside function and outside function Discussions

Write discussion on Inside function and outside function
Your posts are moderated
Related Questions
if a+1/b=b+1/c=c+1/a then the value of abc is

What is a scatter diagram? A scatter diagram is a graphical representation of data points for a particular sample. Choosing a dissimilar sample or enlarging the original one ca

Julia must do a 70:30 split of all of her profits with the Department of Athletics. Julia also has the ability to sell soft drinks. If she decide to sell soft drinks, she must agre


Celine deposited $505 into her savings account. If the interest rate of the account is 5% per year, how much interest will she have made after 4 years? Use the formula F = 9/5

prove that - there is one and only one circle passing through three non - collinear points

i have many trouble in this subject

These can be expressed in terms of two fundamental operations of addition and multiplication. If a, b and c are any three real numbers, then;     1.

Find out the roots of the following quadratic equation. 3x 2 + 7x = 0 Solution: Using Equation 6, one root is determined. x = 0 Using Equation 7, substitute the

How long does it take for an amount of money P to double itself if it is invested at 8% interest compounded 4 times a year?