Change of angle if refractive index changes for 10^-6

[AncientOne99]

Homework Statement

The following expression sin ϑ = 1 / n applies to the angle of total reflection at the transition of the beam from glass to air. For how much
changes the angle if the refractive index changes by 10^−6?
For n take 1.5. Express the result only with n.

Relevant Equations

sin(ϑ) = 1/n(water)

Solution:
(delta (ϑ)) =
-(minus delta n) /(n*sqrt((n^2-1)))

 

[kuruman]

If you are asking whether your answer is correct, it is.

 

[AncientOne99]

Yes i know the solution, but i don't know the steps.

 

[kuruman]

Do you know how to take differentials? For example
$d(x^2)=\frac{d}{dx}(x^2)dx=2xdx.$

Apply this idea to find $d(\sin\theta)$ and $d(\frac{1}{n})$ and set them equal.

 

[AncientOne99]

Do you know how to take differentials? For example
$d(x^2)=\frac{d}{dx}(x^2)dx=2xdx.$

Apply this idea to find $d(\sin\theta)$ and $d(\frac{1}{n})$ and set them equal.

Yes, i know how to take the diferentials, but there is no equation to diferentiate or i don't know it.

 

[AncientOne99]

I solved it, thanks for your help !