Question 1034951
<font face="Times New Roman" size="+2">


You need the Sum Rule:


If *[tex \LARGE \ \ \ \ \ \ \ \ \ \ y(x)\ =\ u(x)\ +\ v(x)]


Then *[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ \frac{du}{dx}\ +\ \frac{dv}{dx}]


The Product Rule:


If *[tex \LARGE \ \ \ \ \ \ \ \ \ \ y(x)\ =\ u(x)\cdot v(x)]


Then *[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ v\frac{du}{dx}\ +\ u\frac{dv}{dx}]


And the Chain Rule:


If *[tex \LARGE \ \ \ \ \ \ \ \ \ \ y\ =\ u(x)]


Then *[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{dy}{dx}\ =\ \frac{dy}{du}\,\cdot\,\frac{du}{dx}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{d}{dx}\left\[xe^{x^2}\ -\ \arcsin\left(\cos(x)\right)\right\]]


So by the Sum Rule


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \frac{d}{dx}\left\[xe^{x^2}\right\]\ -\ \frac{d}{dx}\left\[\arcsin\left(cos(x)\right)\right\]]


For the first term, you need the Product Rule, and for the second term, the Chain Rule:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ \frac{d}{dx}\left\[x\right\]\,\cdot\,e^{x^2}\ +\ x\,\cdot\,\frac{d}{dx}\left\[e^{x^2}\right\]\ -\ \frac{1}{\sqrt{1\,-\,\cos^2x}}\,\cdot\,\frac{d}{dx}\left\[\cos(x)\right\]]


The second term requires another application of the Chain Rule:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ e^{x^2}\ +\ x\,\cdot\,e^{x^2}\,\cdot\,\frac{d}{dx}\left\[x^2\right\]\ -\ \frac{-\sin(x)}{\sqrt{1\,-\,\cos^2x}}]


Finally,


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ e^{x^2}\ +\ 2x^2e^{x^2}\ +\ \frac{\sin(x)}{\sqrt{1\,-\,\cos^2x}}]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
<img src="http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg">
*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \  

</font>