# Math Help - derivative

1. ## derivative

cos^2(1-2x+x^2)

would this be sin^2(1-2x+x^2)*(-2+x^2)?

2. Originally Posted by Asuhuman18
cos^2(1-2x+x^2)

would this be sin^2(1-2x+x^2)*(-2+x^2)?
No! $- 2 \cos(x^2-2x+1) \sin(x^2-2x+1) (2x-2)$.

3. Originally Posted by Danny
No! $- 2 \cos(x^2-2x+1) \sin(x^2-2x+1) (2x-2)$.
could you please tell me how you got this?
thanks

4. Originally Posted by Asuhuman18
could you please tell me how you got this?
thanks
If $y = \cos^2 (x^2-2x+1)$ then let $u = x^2-2x+1$ so $y = \cos^2 u.$ Let $v = \cos u$ so $y = v^2$. Now the chain rule

$
\frac{dy}{dx} = \frac{dy}{dv} \cdot \frac{dv}{du} \cdot \frac{du}{dx}
$

Put in the pieces and back substitute.