If tan(x+y)=x, then determine dy/dx

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justaguide | College Teacher | (Level 2) Distinguished Educator

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It is given that tan (x + y) = x. To determine` dy/dx` use implicit differentiation.

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

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

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

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

=> `dy/dx = -sin^2(x + y)`

 

The derivative `dy/dx = -sin^2(x + y)`

Here is more on implicit differentiation.

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