What is the derivative of x = tan (x+y)

Brooke Richard

Brooke Richard

Answered question

2022-11-16

What is the derivative of x = tan ( x + y )

Answer & Explanation

Maffei2el

Maffei2el

Beginner2022-11-17Added 20 answers

Consider y as a function of x and get (deriving both sides with respect to x):
1 = [ 1 cos 2 ( x + y ) ] [ 1 + d y d x ] (Chain Rule for tan)
Rearranging:
1 + d y d x = cos 2 ( x + y )
d y d x = cos 2 ( x + y ) - 1
d y d x = - ( 1 - cos 2 ( x + y ) ) = - sin 2 ( x + y )

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