Question

Question #9cdcc

Answer 1

`4x`

Explanation:

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

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`