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## Homework Statement

Differentiate the following with respect to x

y = [itex]\frac{4}{x^{3}}[/itex] + [itex]\frac{x^{3}}{4}[/itex]

## The Attempt at a Solution

So the problem here is really getting this into a form that is easy to differentiate and i'd just like to show what i'm doing before I go ahead and do the rest of my questions. The step i'm least confident with is applying chain rule to each term separately...

I want to use the chain rule here, so I would rearrange to this;

y = (x

^{3})

^{-4}+ (4)

^{-x3}

dy/dx = -4(x

^{3})

^{-5}3x

^{2}- x

^{3}(4)

^{-x3-1}.0

dy/dx = -4(x

^{3})

^{-5}3x

^{2}

dy/dx = -12x

^{2}(x

^{3})

^{-5}

(made irrelevant by discussion below)

So, is this ok? I am concerned that my second term disappears, but that's what it looks like I have to do.

Thanks for any help you can give!

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