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### Rate of Change of a Function

```
Date: 6/10/96 at 19:15:55
From: Anonymous
Subject: Rate of change

I'm stuck on this problem:

The rate of change of the function f(x) = sin x + csc x with
respect to change in the variable x is given by the expression
cos x - csc x cot x. Show that the expression for the rate of
change can also be given by -cos x cot^2 x.
```

```
Date: 6/11/96 at 19:34:35
From: Doctor Anthony
Subject: Re: Rate of change

dy/dx = cos(x) - (1/sin(x) * cos(x)/sin(x))

= cos(x){1 - 1/sin^2(x)}

= cos(x){(sin^2(x)-1)/sin^2(x)}

= cos(x){-cos^2(x)/sin^2(x)}

= -cos(x)cot^2(x)

-Doctor Anthony,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
High School Calculus

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