Given y^2 = tan x, what is dy/dx

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justaguide eNotes educator| Certified Educator

It is given that `y^2 = tan x` . To determine `dy/dx` use implicit differentiation.

`y^2 = tan x`

`(d(y^2))/dx = (d(tan x))/dx`

=> `2*y*(dy/dx) = sec^2x`

=> `dy/dx = (sec^2x)/(2*y)`

=> `dy/dx = (sec^2x)/(2*sqrt(tan x))`

The required derivative `dy/dx = (sec^2x)/(2*sqrt(tan x))`

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