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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Help finding a derivative.

**Physics Forums | Science Articles, Homework Help, Discussion**