How to differentiate arctan (x/y) with respect to y?

In summary, the conversation is about differentiating the arctan function with respect to y and the correct formula for it. The person was having trouble generating the correct formula using LaTeX, but it was determined that the formula -x/(x²+y²) is correct.
  • #1
mmh37
59
0
DOES ANYONE SEE WHY MY LATEX FORMULAE ARE NOT BEING GENERATED?

I was wondering how one can differentiate the following:

[tex] arctan (x/y) [/tex]

wrt y

is it just inner times outer derivative, i.e.

[tex] (-x) /((1 + x^2/y^2)*y^2) [/tex]

in the definitions I found they just gave examples like

[tex] tan^(-1) y [/tex]

thanks very much
 
Last edited:
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  • #2
mmh37 said:
DOES ANYONE SEE WHY MY LATEX FORMULAE ARE NOT BEING GENERATED?
LaTeX is currently down but I was able to follow your problem through the code.

If x and y are independant variables then you differentiate wrt to y, just by using the chain rule.
Your answer is correct and can be simplified to -x/(x²+y²).
 

FAQ: How to differentiate arctan (x/y) with respect to y?

What is the definition of the inverse trig derivative?

The inverse trig derivative is the mathematical operation that determines the slope of the tangent line to a curve at a specific point by using the inverse trigonometric functions such as arccosine, arcsine, and arctangent.

How do you find the inverse trig derivative?

The inverse trig derivative can be found by using the formula:

d/dx(arcsin(u)) = 1/sqrt(1-u^2)
d/dx(arccos(u)) = -1/sqrt(1-u^2)
d/dx(arctan(u)) = 1/(1+u^2)
where u is the function inside the inverse trigonometric function.

What is the relationship between inverse trig derivatives and regular trig derivatives?

The relationship between inverse trig derivatives and regular trig derivatives is that they are essentially inverse operations. The inverse trig derivative gives the angle measure, while the regular trig derivative gives the slope of the tangent line at that angle measure.

Why is it important to know how to find the inverse trig derivative?

It is important to know how to find the inverse trig derivative because it is a crucial step in solving problems involving trigonometric functions. It also helps in finding the slope of a curve at a specific point, which is useful in many fields of science and engineering.

What are some common mistakes when finding the inverse trig derivative?

Some common mistakes when finding the inverse trig derivative include forgetting to use the chain rule, forgetting to apply the derivative to the inside function, and not simplifying the final answer. It is also important to remember to use the correct derivative formula for each inverse trig function.

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