1. hartnn

do you mean $$\Large W = \arcsin (x/a)$$ and you want to find its derivative with respect ot x ?

2. hartnn

**to x

3. En

$w=\frac{ Arcsin \alpha }{ \alpha}$ its written that way in my book and it asks for its derivative..

4. hartnn

do you know quotient rule of derivative?

5. En

not really... can you explain it ?

6. En

.. is it the the denominator be squared then the multiply the denominator with the derivative of the numerator minus the numerator time the derivative of the denominator...

7. hartnn

yes

8. hartnn

$$\Large \left[\frac{f(x)}{g(x)}\right]'=\frac{g(x)f'(x)-f(x)g'(x)}{[g(x)]^2}.$$

9. En

i already knew that one.. but my book says that the answer to the problem is zero... i dont get it

10. hartnn

in our case, f(x) = arcsin x g(x) =x what is f'(x) and g'(x) ?

11. hartnn

oh

12. hartnn

derivative of a constant is 0. so maybe your text book is not asking for the derivative with respect to $$\alpha$$

13. hartnn

for any other variable, W will be a constant, and the derivative will be = 0

14. En

why is it that the W is a constant?

15. hartnn

because W is the function of $$\alpha$$ only if $$\alpha$$ is NOT a variable, then W is also not a variable