Question

How do you use the quotient rule to differentiate `(x) / sqrt (1-x^2)`?

Answer 1

`d/(dx) (x/sqrt(1-x^2)) = frac 1 ((1-x^2)^(3/2)`

Explanation:

The quotient rule states that:

#d/(dx) (f/g) = (g((df)/(dx)) -f((dg)/(dx)))/g^2#

Applying to our function:

#d/(dx) (x/sqrt(1-x^2)) = (sqrt(1-x^2)((dx)/(dx)) -x((d(sqrt(1-x^2)))/(dx)))/(sqrt(1-x^2))^2=(sqrt(1-x^2) -x(-2x*1/2*1/sqrt(1-x^2)))/(sqrt(1-x^2))^2=(sqrt(1-x^2) +x^2*1/sqrt(1-x^2))/(sqrt(1-x^2))^2=frac 1 ((1-x^2)^(3/2)#