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Kyle Sutton

Kyle Sutton

Answered question

2022-07-01

If 3 x 2 = tan y, then what is d y d x ?

Answer & Explanation

Bruno Dixon

Bruno Dixon

Beginner2022-07-02Added 14 answers

We use
( tan x ) = sec 2 x
tan 2 x + 1 = sec 2 x
3 x 2 = tan y
sec 2 y = 1 + tan 2 y = 1 + ( 3 x 2 ) 2 = 1 + 9 6 x 2 + x 4
Differentiating both sides
2 x = sec 2 y d y d x
d y d x = 2 x sec 2 y
= 2 x x 4 6 x 2 + 10

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