## avshvk Group Title find by first principle the derivative of arccos(x) / x Pls help anyone?? one year ago one year ago

1. avshvk Group Title

$\cos^{-1} (x) / x find the derivative by first principle???$

2. Goten77 Group Title

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3. Goten77 Group Title

does this mean we cant use the quotient rule?

4. avshvk Group Title

it should be done only by first principle method and not using the formula

5. whpalmer4 Group Title

$\frac{dy}{dx}=\lim_{h \rightarrow 0}\frac{f(x+h)-f(x)}{h}=\lim_{h \rightarrow 0}\frac{1}{h}(\frac{\cos^{-1}(x+h)}{x+h}-\frac{\cos^{-1}(x)}{x})$ Grind out the work...

6. avshvk Group Title

after this what next how to resolve the RHS, pls help

7. whpalmer4 Group Title

I'd start by making a common denominator for the right hand side...

8. avshvk Group Title

Pls give me the steps i'm not getting it.

9. klimenkov Group Title

Reduce this:$\frac{\cos^{-1}(x+h)}{x+h}-\frac{\cos^{-1}(x)}{x}$.

11. avshvk Group Title

yes this is correct answer but it should be done with first principle method

12. nitz Group Title

the method suggeested by @whpalmer4 is right

13. avshvk Group Title

yes but how do we go further to get the answer?