Simplifying the Derivative of a Complex Rational Function

[mattmannmf]

find derivative of

y=(sqrt(8x^4-5))/ (x-1)

ok...after working out the tricky calculations i get for my final answer:

(32x^4sqrt(8x^4-5)-64x^3sqrt(8x^4-5)) / (16x^6-32x^5+ 16x^4-10x^2+20x-10)

I don't know if you want to do the math...im just wondering if i can simplify it anymore. thanks

 

[Mark44]

I'm pretty sure you didn't do this problem the way you were supposed to. Judging by the title of the thread, you are supposed to do logarithmic differentiation, and I don't see any evidence that you have done this. Instead, it looks like you used the chain rule first and then the quotient rule.

$$y~=~\sqrt{\frac{8x^4 - 5}{x - 1}}$$
$$\Rightarrow ln(y)~=~ln \left(\sqrt{\frac{8x^4 - 5}{x - 1}}\right )$$
Use the properties of logarithms to write the right side as a difference, and then differentiate with respect to x.

 

[mattmannmf]

well what i did was (going from your previous equation):

ln(y)= ln(sqrt(8x^4-5)) - ln(x-1)...then i just took the derivative and it pretty much eliminated all the ln

 

[mattmannmf]

well what i did was (going from your previous equation):

ln(y)= ln(sqrt(8x^4-5)) - ln(x-1)...then i just took the derivative and it pretty much eliminated all the ln

 

[Mark44]

On the left side of the equation you should get 1/y * y'. Did you forget to use the chain rule?

 

[mattmannmf]

oh no...i added that... i just forgot to put it up in my above equation