Question #9cdcc

2 Answers
Oct 15, 2017

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

Oct 15, 2017

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