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The function y= `sqrt(tanx)` . The derivative of y can be found by using the chain rule.
y' = `(1/2)(tan x)^(-1/2)*sec^2 x`
=> `1/(2*sqrt(tan x)*cos^2x)`
The derivative for y is not defined for values of x for which the value of tan x is not positive as the square root of a negative number is not a real number.
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