Chain,product or quotient rule? why

[ibysaiyan]

Homework Statement

Hi all well basically i have finished off chain rule and right now i am going through product rule and quotient, as i was going through some questions , i understood the basic rule and so on, but why i don't get is, how do i figure which rule i need to apply given equation using these three rules. For instance : y= x^3 sinx or y=x^3 / sinx , why would it be wrong to apply chain rule? Thanks for your replies ;) (grr i got to figure out using Latex =/)

Homework Equations

The Attempt at a Solution

 

[rock.freak667]

For things in the form y=UV, use product rule

y=u/v use quotient rule (yes you can use the product rule as well, but using this directly is simpler.

You use the chain rule for when you have functions which have exponents that are difficult or tedious to expand, example:

y=(x+1)¹⁹⁷¹²

clearly this is tedious, but the chain rule makes it easier to get the derivative.

 

[Mark44]

Homework Statement

Hi all well basically i have finished off chain rule and right now i am going through product rule and quotient, as i was going through some questions , i understood the basic rule and so on, but why i don't get is, how do i figure which rule i need to apply given equation using these three rules. For instance : y= x^3 sinx or y=x^3 / sinx , why would it be wrong to apply chain rule? Thanks for your replies ;) (grr i got to figure out using Latex =/)

The chain rule should be applied to composite functions, such as f(x) = sin(x^3). To evaluate f(b), for example, you first have to cube b, and then take the sine of that value.

y = x^3 * sin(x) is a product. Use the product rule.
y = x^3/sinx is a quotient. Use the quotient rule. Neither of these functions is composite, so it would be incorrect to apply the chain rule.

Sometimes you'll run across functions that seem likely candidates for a rule, but are not. For example, g(x) = x^2/5 is certainly a quotient. If you needed the derivative, you could use the quotient rule, but that's not advisable. Instead, think of this as (1/5)*x^2 and use the constant multiple rule, which says that d/dx(k*f(x)) = k*d/dx(f(x)). You should never use the quotient rule if the denominator is a constant. It's not that it will give you an incorrect derivative, but rather, that it's somewhat more complicated to use, and you are more likely to make a mistake. Even if you don't make a mistake, you are doing more work than you need to do, and life is short.

 

[ibysaiyan]

Oh,Thanks a lot you two.Now i get it.