# small correction in formula

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Posted by T.Gracken on October 18, 2002 at 10:10:01:

In Reply to: Re: Trouble Learning to Differentiate Equations posted by Brad Paul on October 17, 2002 at 20:02:22:

: : Hi,

: : If I need to differentiate (1/x^3)

: : Is this right:
: : 3x^2/x^6? = 3/x^4

: : Or do I need to apply the power rule to the top and bottom halfs before simplifying? How do you know when to stop?

: : Also, you cannot differentiate the cubed root of a variable, can you?

: There are two simple ways to do this derivative. One is to use what is
: called the quotient rule and the other is to rewrite and do it
: straight. Personally I avoid the quotient rule only because I can't
: remember it. I'm a fan on remembering the lest number of rules. The
: quotient rule is one of those rules that is easily derived from simple
: calculus knowledge. That said let me rewrite the question:

: Dx(1/x3)=Dx(x-3)

: Now it looks easer.

:
: Dx(x-3)=-3 x-4

: Where I used:

: Dx(xn)=n* x n-1

Mr.Paul's way of rewriting the original expression si extremely useful, even when roots are involved!

i.e. if f(x) = cuberoot(x), then rewrite as f(x) = x1/3 and use the same formula for the derivative.

: I see you used the quotient rule but just forgot the "-" between the
: two terms in the numerator.

: Any function that is piece wise continuous has a well defined
: derivative along the pieces. However, it may not be possible to find a
: closed analytical function for the derivative.

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