## jkristia 2 years ago Problem 5A-3g, is the answer correct?

1. jkristia

I'm not able to get the same nice clean answer as in the solution, and I think the problem is a mistake in the given solution where he get $\frac{dy}{dx} \frac{x}{\sqrt{1 - x^2}} = (1-x^2)^{-3/2} ??$ it seems like he forgot the $$x$$ in the numerator I get $=\frac{-x^2+x+1}{(1-x^2)\sqrt{1-x^2}}$ What am I missing, where is my mistake ?

2. OBMD

First change the equation to $\frac{ dy }{ dx}x(x-x ^{2})^{-\frac{ 1 }{ 2 }}$ Use the product rule you get $(1)(1-x ^{2})^{-\frac{ 1 }{ 2 }}+x(-\frac{ 1 }{ 2 })(1-x ^{2})^{-\frac{3 }{ 2 }}(-2x)$ this can be simplified to $\frac{ 1-x ^{2} }{(1-x ^{2})^{\frac{3}{2}} }+\frac{ x ^{2} }{(1-x ^{2})^{\frac{3}{2}} }$ which equals $\frac{ 1 }{ (1-x ^{2} )^{\frac{ 3 }{ 2 }}}$ or$(1-x ^{2})^{\frac{ -3 }{ 2 }}$

3. OBMD

Note that $(1-x ^{2})^{-\frac{ 1 }{ 2 }}=\frac{ 1 }{ (1-x ^{2})^{\frac{ 1 }{ 2 }} }=\frac{ 1-x ^{2} }{ (1-x ^{2})^{ \frac{ 3 }{ 2 } }}$

4. jkristia

oh man.... you are right :). I have to go back and check my calculation, but I think my silly mistake was to multiply by (-2), not (-2x), arghhh... sometime you just go blind staring at a problem.