Question

use logarithmic differentiation to find the derivative of the function y= sin^2 X * tan^4 X/(x^2+1)^2

Answer 1

\(y= (sin^2 x) (tan^4\frac{x}{(x^2+1)^2}\))
Well, \(ln (ab)=ln a + ln b\)
and also \(ln y^n=n ln y\)
Have you attempted it?

Answer 2

yes i have....thats not the equation .... y= (sin^2 x)(tan^4 x)/(x^2+1)^2

Answer 3

Oh.That look much less complicated and easier.
so
\( ln y = 2 ln sin x + 4 ln tan x - ln(x^2 + 1)^2\)
where \(\frac{d(ln y)}{dx}=\frac{y'}{y}\)
So where were you stuck?

Answer 4

i got....4(secx)^2 *(sinx)^2*(tanx)^3/(x^2+1)^2.....so i really didnt know how to incorparate log....so i took a difference route

Answer 5

Ah. okay. As shown above, all you have to do is:
example:
\(\frac{d(ln sin x )}{dx}= \frac{cos x}{sin x} \)

Answer 6

differentiate the term then put it on top of itself.
You'll get something like this
\(y' = y(2cot x + 8 csc 2x +\frac{4x}{x^2 + 1})\)