Name: Basic derivative rules: find the error | Derivative rules | AP Calculus AB | Khan Academy
Uploaded: 2022-07-12T12:31:20.000Z
Duration: 4 min 45 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...

- [Voiceover] So we have two examples here

of someone trying to find the derivative of an expression.

"of seven minus five x using basic differentiation rules.

differentiation rules exercise on Khan academy,

and I thought I would just do them side by side,

because we can kind of think about what each of these

we have a constant and then we have a first degree term,

She took, she's separately taking the derivative of seven,

and separately taking the derivative of five x.

So this my spider senses already going off here,

because what happened to this negative right over here?

So it would've sense for her to do the derivative

of seven, and she could've said minus the derivative,

of five x, that's one possibility that she could've done.

The derivative of a difference is equal to

the derivative, she could've said this was equal to

These two things would've been equivalent to this one.

So I think she had a problem right at step one.

Now, if you just follow her logic after step one,

let's see if she makes any more mistakes.

So, she takes the derivative of a constant,

so constant isn't going to change with respect to x.

So that makes sense, that that derivative is zero.

And so we still have the derivative of five x,

and remember, it should've been negative five x,

the derivative of a constant times something,

And then, she finds the derivative with respect to x

if the slope, if you had the graph of y equals x,

So she clearly made a mistake at step one,

this right of here, should've been a negative,

that's a negative, then that would've been a negative.

And then her final answer should have been,

To see if she made any mistakes and where.

So she's differentiating a similar expression,

so first she takes the derivative of the constant,

plus the derivative of the first degree term.

Derivative of constant is zero, that looks good.

and then you have the derivative of the first degree term.

She is assuming that the derivative of a product

is equal to the product of the derivatives.

And especially, and if you have a constant here,

there's actually a much simpler way of thinking about it.

Frankly the way that Avery thought about it,

to the derivative of a constant times an expression,

is equal to the same thing as the constant

So this would've been the correct way to go,

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Basic derivative rules: find the error | Derivative rules | AP Calculus AB | Khan Academy

assume

equivalent

figure

constant