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Answer 1 · 2017-10-15T14:41:17

$4x$

well, the radical signs are unnecessary. $sqrt(1) = 1$

...so you can rewrite as:

$1 - x^2 - x - x^2 + x$

...and I think this simplifies to:

$1 - 2x^2$

And the derivative of this would b:

$-4x$

GOOD LUCK

Answer 2 · 2017-10-15T14:49:59

Given: $sqrt1-x^2-x/sqrt1-x^2+x$

Use the substitution, $sqrt1 = 1$ :

$1-x^2-x-x^2+x$

Combine like terms:

$1-2x^2$

Differentiate:

$(d(1-2x^2))/dx = (d(1))/dx -(d(2x^2))/dx$

The first term is 0 because the derivative of a constant is 0:

$(d(1-2x^2))/dx = - (d(2x^2))/dx$

Use the linear property of the derivative:

$(d(1-2x^2))/dx = - 2(d(x^2))/dx$

Use the power rule, $(d(x^n))/dx = nx^(n-1)$ :

$(d(1-2x^2))/dx = - 4x$