Question

Can someone help me with 5A-3 (g)? I'm checking my solution and don't see how they got the derivative of x/sqrt(1-x^2).

Answer 1

I believe you can apply the quotient rule here:\[f(x) =\frac{ x }{ \sqrt{1-x ^{2}} }\]\[f(x) = \frac{ g(x) }{h(x)}, x \neq 0\]\[f \prime(x) = \frac{ g \prime(x)h(x)-g(x)h \prime(x) }{[h(x)]^{2} }\]\[ = \frac{ (1\times \sqrt{1-x^2})-(x \times \frac{ 1 }{ 2\times \sqrt{1-x^2} }) }{ 1-x^2 }\]