Question

can someone solve this for me and show their work step by step, please ?
derivative of radical{(x-1)/(x+1)}

Answer 1

\[\sqrt\frac{x-1}{x+1}\]To rationalise the denominator
Multiply by a special form of one
\[=\sqrt\frac{x-1}{x+1}\times1\\
=\frac{\sqrt{x-1}}{\sqrt{x+1}}\times\frac{\sqrt{x+1}}{\sqrt{x+1}}\]

Answer 2

i' sorry, i forgot to type that I was looking for the derivative

Answer 3

oh right

Answer 4

you could use the quotient rule (that's always fun)

\[\left(\frac{u}{v}\right)'=\frac{u'v-v'u}{v^2}\]

Answer 5

There is no reason to rationalise the denominator now
\[u=\sqrt{x-1}\implies u'=\]\[v=\sqrt{x+1}\implies v'=\\
\qquad\qquad\quad\implies v^2=\]

Answer 6

Thanks!

Answer 7

and it might be easier if you express the square roots as indices ^(1/2)