Hello. I have been trying to find this derivative from first principles for at least a couple hours, but just can't make any progress with it.(adsbygoogle = window.adsbygoogle || []).push({});

Find the derivative of[tex]3x-\frac{5}{x}[/tex]

Well I start by saying that the derivative is the limit as h approaches 0 of

[tex]\frac{f(x+h)-f(x)}{h} [/tex] where h=deltax

Then I go on to say that this is equal to the limit as h approaches 0 of

[tex]\frac{3h-\frac{5}{x+h}+\frac{5}{x}}{h} [/tex]

I then simplify by taking h out of the numerator by factoring and then cancel h on the numerator and denominator. This the derivative equals the limit as h approches 0 of

[tex]3-\frac{5}{(x+h)h}+\frac{5}{xh} [/tex]

As you can see, my derivative is now a bloody mess and I see no way of getting h out of the denominator. Please help! By the way I need to do this from first principles (dy/dx=(f(x+h)-f(x))/(h) ). Thankyou! :surprised

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# Help finding a derivative.

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