Re: Trouble Learning to Differentiate Equations

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Posted by Brad Paul on October 17, 2002 at 20:02:22:

In Reply to: Trouble Learning to Differentiate Equations posted by Mary on October 17, 2002 at 19:26:40:

: 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:

D_x(1/x³)=D_x(x^-3)

Now it looks easer.

D_x(x^-3)=-3 x^-4

Where I used:

D_x(xⁿ)=x ^n-1

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.

Follow Ups:

small correction in formula T.Gracken 10:10:01 10/18/02 (2)
- Thanks for checking (n/t) Brad Paul 12:31:19 10/18/02 (1)
  - no problemo. I'm sure you will correct my typos too. T.Gracken 19:19:57 10/18/02 (0)

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Comments:
: : 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: : Dx(1/x3)=Dx(x-3) : Now it looks easer. : : Dx(x-3)=-3 x-4 : Where I used: : Dx(xn)=x n-1 : 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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