inverse TRIG : ( (1 Viewer)

[hello-there]

Differentiate:
1. sin(tan^-1(x))

2. tan^-1(sinx)

3. Ln (tan^-1 (x/2))

THANX

 

[the-derivative]

Side note: When I did inverse trig, I got taught that [tan^-1 (u)]' = u' / (1+u^2), so that should make things easier.

 

[Loneliness is]

last one is fuckang eazy

 

[hello-there]

How do you draw inverse trig?

such as y=1/square root(9-x^2)

 

[the-derivative]

How do you draw inverse trig?

such as y=1/square root(9-x^2)

Can't you just use normal calculus sketching methods?
Like find the domain, range, then differentiate it to find stationary points, then test points to determine the nature of the curve etc etc.

Whereas if you were asked to draw stuff like sin, cos, tan inverse or stuff like that, just remember since it's the inverse, so the domain becomes the range and vice verca. E.g. for tan^-1 (x,) the domain is all values of x, and the range would be between -pi/2 and pi/2

 

[xV1P3R]

You could take it as a transformation of y = sqrt(9-x²) which is a semicircle with radius 3.

Where y = sqrt(9-x²), there is an asymptote because 1/0 does not exist. But as the semicircle approaches 0, the graph approaches infinity if you see what I mean.