How do you differentiate tan 2x = cos 3y

amacorrit80

amacorrit80

Answered question

2022-07-18

How do you differentiate tan 2 x = cos 3 y

Answer & Explanation

bgr0v

bgr0v

Beginner2022-07-19Added 13 answers

Using the chain rule, where u = 2 x and d d x = d d u d u d x
d d u ( tan ( u ) ) d u d x = d d x ( cos ( 3 y ) )
sec 2 ( u ) 2 = d d x ( cos ( 3 y ) )
2 sec 2 ( 2 x ) = d d x ( cos ( 3 y ) )
Using the chain rule, where v = 3 y and d d x = d d v d v d y d y d x
2 sec 2 ( 2 x ) = d d v ( cos ( v ) ) d d y ( 3 y ) d y d x
2 sec 2 ( 2 x ) = - 3 sin ( v ) d y d x
- 2 sec 2 ( 2 x ) csc ( 3 y ) 3 = d y d x

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