What is the derivative `dy/dx` given that : x = tan y

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justaguide | College Teacher | (Level 2) Distinguished Educator

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It is given that x = tan y. To determine the derivative `dy/dx` , use implicit differentiation.

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

=> `dy/dx = 1/(sec^2 y)`

=> `dy/dx = 1/(1 + tan^2y)`

=> `dy/dx = 1/(1 + x^2)`

The derivative `dy/dx = 1/(1 + x^2)`

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