Finding the derivative, quotient rule with natural log function.

HHenderson90
Messages
9
Reaction score
0

Homework Statement



Find y' of
y= 1-3ln(7x)/x^4

Homework Equations


The Attempt at a Solution


I used the quotient rule and got:
y'=x^4*d/dx(1-3ln(7x)-(1-3ln(7x)*d/dx(x^4)/(x^4)2

which is: x^4*(0-3*1/7x*7)-(1-3ln(7x))*4x^3/x^8
simplified to: 3x^4/x-1+3ln(7x)*4x^3
3x^3-4x^3+12x^3ln(7x)/x^8
take out the x^3 from the denominator and the numerator and I get the answer:

y=-1+12ln(7x)/x^5
The website I use to do my calculus homework says this is wrong, where is my error?
 
Physics news on Phys.org
HHenderson90 said:

Homework Statement



Find y' of
y= 1-3ln(7x)/x^4

Homework Equations





The Attempt at a Solution


I used the quotient rule and got:
y'=x^4*d/dx(1-3ln(7x)-(1-3ln(7x)*d/dx(x^4)/(x^4)2

which is: x^4*(0-3*1/7x*7)-(1-3ln(7x))*4x^3/x^8
simplified to: 3x^4/x-1+3ln(7x)*4x^3
3x^3-4x^3+12x^3ln(7x)/x^8
take out the x^3 from the denominator and the numerator and I get the answer:

y=-1+12ln(7x)/x^5
The website I use to do my calculus homework says this is wrong, where is my error?

You dropped a minus sign. You should get -3x^3-4x^3. Not 3x^3-4x^3.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top