Find the derivative of y = tan 2 x ?

Jamir Summers

Jamir Summers

Answered

2022-11-26

Find the derivative of y = tan 2 x ?

Answer & Explanation

Melanie Wong

Melanie Wong

Expert

2022-11-27Added 11 answers

d y d x = d d x ( tan 2 x )
y = f ( g ( x ) )
d f ( g ( x ) ) d x = d d ( g ( x ) ) f ( g ( x ) ) × d d x g ( x )
Here f ( g ( x ) ) = tan ( x ) 2 and g ( x ) = tan ( x )
d d x ( tan ( x ) ) 2 = d d ( tan ( x ) ) ( tan ( x ) ) 2 × d d x ( tan ( x ) )
d d x ( tan 2 ( x ) ) = 2 tan ( x ) × d d x ( tan x ) d y d x = 2 tan ( x ) × sec 2 ( x ) d d x tan x = sec 2 x d y d x = 2 sec 2 x tan x
Hence, the derivative of y = tan 2 x is d y d x = 2 sec 2 x tan x

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