How do I find the derivative of #F(x)=arcsin(sqrtsinx)#?

1 Answer
Sasha P.
Oct 27, 2015

#F'(x)=cosx/(2sqrt(sinx)sqrt(1-sinx))#

Explanation:

#F(x)=f(g(x)) => F'(x)=f'(g(x))*g'(x)#

#F'(x)=1/sqrt(1-(sqrt(sinx))^2)*(sqrt(sinx))'#

#F'(x)=1/sqrt(1-(sqrt(sinx))^2) * 1/(2sqrt(sinx)) * (sinx)'#

#F'(x)=1/sqrt(1-sinx) * 1/(2sqrt(sinx)) * cosx#

#F'(x)=cosx/(2sqrt(sinx)sqrt(1-sinx))#

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