Let's do a simpler one so you can see the method.

Differentiate x^6 wrt x^2:

Say y = x^6, t =x^2

Now

Plugging in:

and that is the answer. There is an even simpler way involving a substitution.

]]>Thanls!]]>

Please help with 2 and 3]]>

Please read this:

http://www.mathisfunforum.com/viewtopic.php?id=14654

Please show a little bit of your work, or at least that you tried.

]]>Answer each of the following:

(1) If y=x+1/x prove that x²(d²y/dx²)+x(dy/dx)=y

(2) Find the second derivative of (2x+3)/(3x-1) with respect ro (x-1)/(x+1)

(3) If y²=8/(1+x²) prove that (x²+1)(d²y/dx²)+3x(dy/dx)+y=0

(4) If y=(√x)+1/√x and z=(√x)-1/√x prove that d²y/dx²=(2x(y+2))/(x+1)³

(5) If y=cosx-3sinx prove that y'''+y''+y'+y=0