Name: Derivative of ln(x) | Advanced derivatives | AP Calculus AB | Khan Academy
Uploaded: 2022-07-12T12:31:34.000Z
Duration: 2 min 3 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

- [Instructor] In this video, we're going to think

about what the derivative with respect to x

And I'm gonna go straight to the punch line.

In a future video, I'm actually going to prove this.

But in this one, we're just going to appreciate

that this seems like it is actually true.

And just to feel good about the statement,

what the slope of the tangent line is at different points.

what does the slope of the tangent line look like?

If x is equal to one, one over one is still one,

and that seems like what we see right over there.

Well, this point right over here is the natural log of two,

but more interestingly, what's the slope here?

let's see, if I try to draw a tangent line,

the slop of the tangent line looks pretty close to 1/2.

If I go right over here, when x is equal to four,

this point is four comma natural log of four,

and if you accept this, it is exactly 1/4,

and you could even go to values less than one.

it does indeed look like the slope is two over there.

with respect to x of the natural log of x, it is one over x.

In a future video, we'll actually prove it.

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Derivative of ln(x) | Advanced derivatives | AP Calculus AB | Khan Academy

slightly

straight

consistent

sense