Thursday

August 21, 2014

August 21, 2014

Posted by **ana** on Monday, May 14, 2012 at 4:15pm.

- logarithmic differentiation -
**Reiny**, Monday, May 14, 2012 at 4:27pmy = [(x^2 + 1)(x^2-1) ]^(1/4)

= (x^4 - 1)^(1/4)

ln y = (1/4) ln(x^4 -1)

(dy/dx) / y = (1/4)(4x^3)/(x^4 - 1)

dy/dx = (1/4)(y)(4x^3)/(x^4 - 1)

or

you can replace y with (x^4 - 1)^(1/4)

and simplify that a bit since the denominator is x^4 - 1

- logarithmic differentiation -
**drwls**, Monday, May 14, 2012 at 4:29pmDo you want the derivative of that? Does the "fourth root" apply to the numerator only, or the complete fraction

(x^2+1)/(x^2-1) ?

You need to write the function in a clear nonambiguous manner, using parentheses where necessary. Use ^1/4 for fourth roots.

- missed the division sign - logarithmic differentiation -
**Reiny**, Monday, May 14, 2012 at 4:45pmSorry ana, my answer is incorrect,

I read that as a multiplication , should have been a division

ln y = (1/4) (ln (x^2 + 1) - ln(x^2 -1)

(dy/dx) / y = (1/4) ( 2x/(x^2+1) - 2x/(x^2 + 1) )

dy/dx = (1/4)(y) (4x)/(x^4 - 1)

= xy/(x^4 - 1)

replace y with the original if you have to.

**Related Questions**

Calculus - I need to find the derivative of the following problem via ...

Calc - Use logarithmic differentiation to find dy/dx. y = sq. root [(x^2 - 1)/(x...

calc - logarithmic differentiation of find derivative of y= square root of x^x

logarithmic differentiation - How do you find the logarithmic differentiation ...

logarithmic differentiation - How do you find the logarithmic differentiation of...

logarithmic differentiation - How do you find the logarithmic differentiation of...

calculus - solve the logarithmic equation. Be sure to reject any value of x that...

calculus - Use logarithmic differentiation: F(x)= (3x+6)^4 (x^3 -2)^5 f'(x)=

Calculus - Use logarithmic differentiation: F(x)= (3x+6)^4 (x^3 -2)^5

pre-calculus - solve the logarithmic equation. be sure to reject any value of x ...