## anonymous 3 years ago find by first principle the derivative of arccos(x) / x Pls help anyone??

1. anonymous

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

2. Goten77

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3. Goten77

does this mean we cant use the quotient rule?

4. anonymous

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

5. whpalmer4

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

6. anonymous

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

7. whpalmer4

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

8. anonymous

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

9. klimenkov

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

10. anonymous

11. anonymous

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

12. anonymous

the method suggeested by @whpalmer4 is right

13. anonymous

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