find derivative of ln sqrt(x^2 + 1) / (x (2x^3 - 1)^2))

[venialove]

Find the derivative of \(\displaystyle f(x)\, = \, ln\frac{\sqrt{x^2 \, + \, \, 1}}{x \cdot (2x^3-1)^2}\)

 

[stapel]

What have you tried? How far have you gotten? Where are you stuck? You took the derivative of the logarithm; then you began to apply the Quotient Rule to the rational expression, and... then what?

Please be complete. Thank you!

Eliz.

 

[skeeter]

\(\displaystyle \ln\frac{\sqrt{x^2+ 1}}{x \cdot (2x^3-1)^2} = \frac{1}{2}\ln(x^2+1) - \ln{x} - 2\ln(2x^3-1)\)

remember the properties of logs? now find the derivative.

 

[venialove]

f''= 1/x+2 (2x)/(x^2+1)-(3x^2)/(2x^3-1)

 

[stapel]

f''= 1/x+2 (2x)/(x^2+1)-(3x^2)/(2x^3-1)

Is this related to the original exercise, or is this a new question...?

Eliz.