# Differentiation

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#1
How do you differentiate arctan2x?
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8 months ago
#2
(Original post by Sidd1)
How do you differentiate arctan2x?

Use the chain rule. For example, let u = 2x.

If we have y = arctan2x, we can rewrite dy/dx as:

dy/dx = dy/du x du/dx

Therefore what is dy/du and du/dx? After obtaining these and multiplying them, the final answer should be in terms of x.
Last edited by GrayestOwl0900; 8 months ago
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#3
(Original post by GrayestOwl0900)
Use the chain rule. For example, let u = 2x.

If we have y = arctan2x, we can rewrite dy/dx as:

dy/dx = dy/du x du/dx

Therefore what is dy/du and du/dx? After obtaining these and multiplying them, the final answer should be in terms of x.
Okay so I did du/dx and got u =2x so u' = 2
Then re-wrote y= arctanu
which can also be written as: u = tany and did du/dy = sec^y and dy/du = 1/sec^y
So, dy/dx = 2/sec^y ... What do I do now? Because they got an answer of 2/1+4x^2 ?

I know I have to use the identity : 1+tan^2 y = sec^y but I still can't get 1+4x^2?

Oh waiitttt hold on y= arctan2x can be written as tany = 2x so using the identity sec^2y = 1 + (2x^2) = 1+4x^2 right okay got it!!!!
Last edited by Sidd1; 8 months ago
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