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Function X is a variable...


Date: 9 Jan 1995 11:01:59 -0500
From: Winnie Fan
Subject: question

Hello Dr. Math,
        I am a student in calculus at Monta Vista High School.  Right now 
we are learning general exponential and logarithmic functions.  In class 
we are giving the formula Dx a^u = a^u ln a * Dx u.  With this formula, I 
am able to do problems where a is a number.  In one of my homework 
problems, we are giving the function f(x) = X^tanX.  Then we are asked to 
find the derivative of the function f(x).  Since in this function X is a 
variable, I am stuck here.  Please help!

                                                               Winnie Fan


Date: 9 Jan 1995 12:46:25 -0500
From: Dr. Ken
Subject: Re: question

Hello there!

You're right, this is a different kind of problem, but you can turn it into
a very similar problem by writing the function in a different form.  Try
this:

x^Tan[x] = e^Ln[x^Tan[x]] = e^(Tan[x] * Ln[x])

And then see if you can handle it from there.  This is the standard way of
dealing with nasty exponents: get them in terms of a constant base.

-Ken "Dr." Math
    
Associated Topics:
High School Calculus

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