What is the derivative of the inverse tan(y/x)?

Chanel Hunter

Chanel Hunter

Answered question

2023-02-15

What is the derivative of the inverse tan(y/x)?

Answer & Explanation

Kamari Potts

Kamari Potts

Beginner2023-02-16Added 10 answers

The derivative would be 1 x 2 + y 2 ( d y d x - y x )
If u is tan - 1 ( y x ) then tan u = y x . Differentiating w.r.t. x,
sec 2 u d u d x = 1 x 2 ( x d y d x - y )
d u d x = cos 2 u [ 1 x 2 ( x d y d x - y ) ]
= x x 2 + y 2
Hence, 1 x 2 + y 2 ( d y d x - y x )

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