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?
: : Please help....thanks.
: 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:
: 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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