determine dy/dx for y= sqrt(tanx) and state any values of x for whcih the function is not differentiable

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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.