How to find the derivative?

[TheNascar92]

I need to find the derivative but WITHOUT the use of the quotient rule:

f(x)= (x^2+5x-1)/(2x^2). Does anyone have any clue on where i should start, in other words how could i do this without the chain rule? Thank you!

 

[mmm4444bot]

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How about decomposing the rational function into a sum of three ratios?

I'll set it up. You simplify it and write the powers of x using negative exponents.

You can then differentiate using only the Power Rule.

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\(\displaystyle \frac{x^2 + 5x - 1}{2x^2} \; = \; \frac{x^2}{2x^2} \; + \; \frac{5x}{2x^2} \; - \; \frac{1}{2x^2}\)

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[TheNascar92]

thank you thats exactly what i needed