En
  • En
please help!!!! find the derivative of W=Arcsin a / a
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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hartnn
  • hartnn
do you mean \(\Large W = \arcsin (x/a)\) and you want to find its derivative with respect ot x ?
hartnn
  • hartnn
**to x
En
  • En
\[w=\frac{ Arcsin \alpha }{ \alpha}\] its written that way in my book and it asks for its derivative..

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hartnn
  • hartnn
do you know quotient rule of derivative?
En
  • En
not really... can you explain it ?
En
  • 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...
hartnn
  • hartnn
yes
hartnn
  • hartnn
\(\Large \left[\frac{f(x)}{g(x)}\right]'=\frac{g(x)f'(x)-f(x)g'(x)}{[g(x)]^2}. \)
En
  • En
i already knew that one.. but my book says that the answer to the problem is zero... i dont get it
hartnn
  • hartnn
in our case, f(x) = arcsin x g(x) =x what is f'(x) and g'(x) ?
hartnn
  • hartnn
oh
hartnn
  • hartnn
`derivative of a constant is 0.` so maybe your text book is not asking for the derivative with respect to \(\alpha \)
hartnn
  • hartnn
for any other variable, W will be a constant, and the derivative will be = 0
En
  • En
why is it that the W is a constant?
hartnn
  • hartnn
because W is the function of \(\alpha\) only if \(\alpha\) is NOT a variable, then W is also not a variable

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