Question #503cb

1 Answer
Nov 8, 2015

dy= (1-2x^2)/(sqrt(1-x^2))dx

Explanation:

Simply find dy/dx first

Using product rule we find the following
dy/dx = x *(sqrt(1-x^2))' + (sqrt(1-x^2))(x)'

dy/dx = x *(sqrt(1-x^2))' + (sqrt(1-x^2))1

dy/dx = x *((-2x)/(2sqrt(1-x^2))) + sqrt(1-x^2)

dy/dx = (-x^2)/(sqrt(1-x^2)) + sqrt(1-x^2)

dy/dx = (-x^2)/(sqrt(1-x^2)) + (1-x^2)/sqrt(1-x^2)

dy/dx = (1-2x^2)/(sqrt(1-x^2))

now just multiply the dx to the other side

dy= (1-2x^2)/(sqrt(1-x^2))dx