What is the derivative of tan^(-1)(4x)?

postkortidvi

postkortidvi

Answered question

2023-03-22

What is the derivative of tan - 1 ( 4 x ) ?

Answer & Explanation

meakQueueksiu7e

meakQueueksiu7e

Beginner2023-03-23Added 5 answers

Derivative of tan - 1 4 x can be written using the formula for the derivative of tan - 1 x = 1 16 x 2 + 1 d d x ( 4 x )
d d x tan - 1 4 x = 1 16 x 2 + 1 d d x ( 4 x )
= 4 16 x 2 + 1
abadunayj6f

abadunayj6f

Beginner2023-03-24Added 5 answers

Step 1
y = arctan ( 4 x )
tan y = 4 x
sec 2 y d y d x = 4
Step 2
( tan 2 y + 1 ) d y d x = 4
( 16 x 2 + 1 ) d y d x = 4
d y d x = 4 16 x 2 + 1

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