Find the differential dy of the given function. (Use "dx" for dx.)
y = x sqrt(1 − x^2)
y = x√(1-x^2)
so, using the product rule,
dy = 1*√(1-x^2) + x * 1/2 * 1/√(1-x^2) * -2x = (1-2x^2)/√(1-x^2)
y = x sqrt(1 − x^2)
so, using the product rule,
dy = 1*√(1-x^2) + x * 1/2 * 1/√(1-x^2) * -2x = (1-2x^2)/√(1-x^2)