-3ln l-2xl/5+2x
Please help.
this shouldl read
-3ln abs -2x over 5+2x
So what do you need? the derivative?
The question reads:
find the derivative of the function y
I've completed several of these and keep coming up with the wrong answer...if you can complete it, and have time, please show as much as you can, so I can see what I am doing wrong. Thanks for the reply.
-3ln l-2xl/5+2x
Please help.
this shouldl read
-3ln abs -2x over 5+2x
=====================
If I assume the derivative is desired and we are talking about:
-3 ln | -2x |
-------------
(5 + 2 x)
there is no such thing as ln of a negative number, so the only effect of the absolute value is to make this work for negative as well as positive x. Do the problem for 2x
bottom*derivative of top - top*derivative of bottom
---------------------------
bottom squared
(5+2x)(-3*2/2x) + 3 ln 2x * 2
-------------------------------
25 +20 x + 4 x^2
-15/x - 6 + 6 ln 2x
--------------------
25+20x + 4 x^2
-15 - 6x + 6 x ln 2x
--------------------
25 x + 20 x^2 + 4 x^3
Oh, and call x the absolute value |x| because we are doing this for the absolute value of x
Thanks Damon....that problem was wrong also...it should have been a negative absolute. that has been my problem all along....I wanted to be sure that my formula and math was correct....and you confirmed that for me. Thanks...I guess I will have to settle for a 90...cause I have a whole nother chapter to complete by April 30th.
To simplify the expression -3ln(|-2x|/(5+2x)), we can follow these steps:
1. Apply the properties of logarithms. Let's start by using the property logₐ(b/c) = logₐ(b) - logₐ(c). In our case, a is e (the base of natural logarithm), b is |-2x|, and c is (5+2x):
-3ln(|-2x|/(5+2x)) = -3ln|-2x| + 3ln(5+2x)
2. Simplify the expression ln|-2x|. Since the logarithm of a negative value is undefined, we need to consider the absolute value of -2x:
ln|-2x| = ln(2x)
3. Substitute back into the original expression:
-3ln|-2x| + 3ln(5+2x) = -3ln(2x) + 3ln(5+2x)
And there you have the simplified expression: -3ln(2x) + 3ln(5+2x).