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differentiate arctan(xy)

How do you do this?

I've been working with partial derviatives recently but i've forgotten simple differentiation rules I learnt at A Level 3 years ago.. :frown:

anyway just need to know how to differentiate arctan(xy). can anyone explain? or show? thank you!!

Reply 1

Farhan.Hanif93

Original post by christykai1049

How do you do this?

I've been working with partial derviatives recently but i've forgotten simple differentiation rules I learnt at A Level 3 years ago.. :frown:

anyway just need to know how to differentiate arctan(xy). can anyone explain? or show? thank you!!

Differentiating w.r.t. what? Is it partial differentiation?

Set

z=\arctan (xy)

and take the tan of both sides.

Reply 2

james22

d/dx of arctanx=1/(x^2+1) then chain rule?

Reply 3

christykai1049

Original post by Farhan.Hanif93

Differentiating w.r.t. what? Is it partial differentiation?

Set

z=\arctan (xy)

and take the tan of both sides.

no, not partial dervatives. i just need to know the differentiation of arctan(xy)

Reply 4

little_wizard123

d(arctan f(x))/dx = f'(x)/(1+f(x)^2).

Edit: This was based on your above post that it's not partial differentiation, i.e. y is not a function of x.

(edited 12 years ago)

Reply 5

Intriguing Alias

Original post by christykai1049

How do you do this?

I've been working with partial derviatives recently but i've forgotten simple differentiation rules I learnt at A Level 3 years ago.. :frown:

anyway just need to know how to differentiate arctan(xy). can anyone explain? or show? thank you!!

\dfrac{d}{dx} \tan^{-1}(x) = \dfrac{1}{x^2+1}[br][br][br]

Then chain rule. To work the above about just differentiate normally using

z = \tan^{-1}(x)

and taking the tan of both sides.

EDIT: Woops beaten to it, oh well.

Reply 6

Farhan.Hanif93

Original post by christykai1049

no, not partial dervatives. i just need to know the differentiation of arctan(xy)

You haven't give us enough information. What are you differentiating with respect to? x? Is y a function of x or is it independent etc. If y is a function of x, follow the advice given to take the tan of both side, differentiate using the chain rule and go from there.