derivative

**Asuhuman18** · October 25th 2009, 01:32 PM

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

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

**Danny** · October 25th 2009, 01:44 PM

Originally Posted by Asuhuman18

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

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

No! $- 2 \cos(x^2-2x+1) \sin(x^2-2x+1) (2x-2)$ .

**Asuhuman18** · October 25th 2009, 02:14 PM

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

**Danny** · October 25th 2009, 03:10 PM

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

$<br /> \frac{dy}{dx} = \frac{dy}{dv} \cdot \frac{dv}{du} \cdot \frac{du}{dx}<br />$

Put in the pieces and back substitute.

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