Visualizing the derivative of sin(x)

A visual of the derivative of f(x)=sin(x). We show how to think about the derivative of a function visually.

#manim #calculus #derivatives #derivative #tangentline #slope #parabola #mathvideo #mathshorts #math #visualmath #graph #sinefunction #trigonometry #linearapproximation

[kirahen]

I've been wondering about this ever since learning about derivatives. Thanks for confirming my suspicion

[akfkml]

i found this out 2 days ago when i was messing around in desmos trying to find the tangent line of a sine function. i knew the graph would be a sine wave of some sort, and i found out that the gradient of the tangent line of sin x = sin x-π/2, which is equal to cos x

[greedskith]

Thnx for this! And have you considered make a "Essence of conic sections geometrically"? There are many old books on internet for free access like geometry of conic sections please have a look at them

[pengin]

I am kind of sad that you chose to present this fact this way, because the derivation of that fact can be seen even nicer in a visual form, by looking at a point P on the unit circle with angle theta from the x-axis and moving it a tiny step Δtheta to obtain P'. Draw a vertical line through P and a horizontal line through P' which intersect at Q to obtain a right triangle PQP' such that angle QPP' ≈ theta. As |PP'| ≈ Δtheta, we obtain that
sin'(theta) ≈ |PQ|/|PP'| ≈ cos(theta). This proof is not rigorous but can easily be made into a rigorous argument.

[shreya...]

My jaw dropped and I don't even know why. I knew what would be the outcome but it still surprised me.

[tarannum]

this is literally the video i have been searching for the past 6 hours

[terra]

Thanks! I am just learning about derivatives and this video helped me understand it a little bit better

[AshishMishra-lgci]

Omg this is the most beautiful explanation of derivatives i have seen

[mrnogot]

“We can see that…” is doing a lot of heavy lifting here

[jetx_]

Nice! Can you show us the derivative for e^x?

[siraaron]

Anyway, to anyone who wants to try this, you can use y=f'(t)(x-t)+f(t), and initialise f(x) as whatever differentiable function you want, and t as a parameter. This function will generate a tangent line on the curve at point (t, f(t)).

This works on desmos btw. If you can't write f'(t), try d/dt(f(t)) instead.

[quantumxam-]

Yoo this is crazy af, l have always been trying to visualize all these but now I found one... Cool

[haythemtilouch]

I'm curious on how you create theese visualisations what software u use ?

[nithinsirimanne]

This is what teaching should be, without letting children memorize everything

[SkalopSkalop-xomj]

dsin(x)/dx =(sin(x+dx) - sin(x)) /dx
=(
/dx

=sin(x)×0 + cos(x) × 1
=cos(x)
[if dx tends to 0 sin(dx) /dx tends to 1 and (cos(dx) - 1)/dx to 0]

[drmay]

Nice, could you tell me please how to compute the slope

[AnglandAlamehnaSwedish]

Wow I forget that it's been almost 20 yrs since I used a derivative in a physical problem

[anadiacostadeoliveira]

To find the derivative, plot in a graph following here:

f(x) = (your common function here)
y = d/dx f(x)

So you get the derivative!

[AhmedulAttar]

Amazing... Which program do you use for animation

[thebester]

You prove it using Sin addition formulae right?