Differentiate the function f(x)=arcsin(sqrtx)

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embizze | High School Teacher | (Level 1) Educator Emeritus

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The derivative of arcsin is `d/(dx)arcsinu=(u')/(sqrt(1-u^2))` where u is a differentiable function of x. Here `u=sqrt(x),(du)/(dx)=1/(2sqrt(x))`

Thus `d/(dx)arcsin[sqrt(x)]=(1/(2sqrt(x)))/sqrt(1-x)` which simplifies to `1/(2sqrt(x)sqrt(1-x))`

** Alternatively you could write it as `1/(2sqrt(x(1-x)))` **


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