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 September 12th, 2009, 02:56 AM #1 Newbie   Joined: Sep 2009 Posts: 1 Thanks: 0 Analysis Question Help I am having trouble completing an analysis question. The equation for the COST of laying power cables is: C=a[8-5tan(30)]+5bsec(30) where 'a' and 'b' are separate costs(\$) for laying the cable underwater and on land respectively. I need to investigate the possible effects of a change in the costs of running the cable under water and/or on land. How would I show and explain my results? I suspect that I need to show some kind of graph...possibly a derivate...?
 September 12th, 2009, 10:39 AM #2 Senior Member   Joined: Dec 2008 Posts: 251 Thanks: 0 Re: Analysis Question Help In finding the partial derivative of $C\,=\,a(8\,-\,5\,\tan\,30^{\circ})\,+\,5b\,\sec\,30^{\circ},$ with respect to $a$ or $b$ we can use the rules $\frac{d}{dx}(f(x)\,+\,g(x))\,=\,f'(x)\,+\,g#3 9;(x)$ and $\frac{d}{dx}\,(kx)\,=\,k.$ Partial differentiation is just like ordinary differentiation, only in differentiating with respect to a variable we treat all other variables as constants. Here is the first step to find $\frac{\partial C}{\partial a}$: $\begin{eqnarray*} \frac{\partial C}{\partial a} &=& \frac{\partial}{\partial a}(a(8\,-\,5\,\tan\,30^{\circ})\,+\,5b\,\sec\,30^{\circ})\\ &=& \frac{\partial}{\partial a}(8a)\,-\,\frac{\partial}{\partial a}(5a\,\tan\,30^{\circ})\,+\,\frac{\partial}{\part ial a}(5b\,\sec\,30^{\circ}). \end{eqnarray*}$

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