Examples of using First derivative in English and their translations into Thai
{-}
-
Colloquial
-
Ecclesiastic
-
Ecclesiastic
-
Computer
This is the first derivative.
So that's the information to tell us about the first derivative.
The first derivative at 0 is 1.
Plus 4 times the first derivative.
So the first derivative of this y prime is equal to A cosine of x.
I'm going to add minus 3 times the first derivative to that.
Well the first derivative of e to the x is still e to the x, 2 e to the x, minus 3 times a function.
So especially at this critical point where the first derivative is 0.
But that's the first derivative of our function.
And remember, those are just the points where our first derivative is equal to 0.
So what is the first derivative of it, first of all.
You could view it as the derivative of the first derivative, right?
So first, let's see where our first derivative is equal to 0, and get our critical points.
The slope is 0 right there, we figured that out, because the first derivative was 0 there.
The first derivative of p of x, this is my current p of x, this constant term, derivative of 0.
The second derivative of y minus 3 times the first derivative y minus 4 times the function.
The first derivative of this quadratic-- but any quadratic can be written like this-- is 2ax plus b.
We know the solution to the second derivative minus 3 times the first derivative minus 4y.
The first derivative of p is going to be, up here, this was the first derivative of p at 0, right?
So the second derivative of y2 is just e to the x plus 2 times the first derivative is what?
A times the second derivative plus B times the first derivative plus C times the function is equal to g of x.
So our first derivative is y prime is equal to-- let's see c1-- 1/2 plus c2-- so it's-- well I will write this first-- it's equal to 2 over 2.
So let's say I had the differential equation y prime prime plus the first derivative plus y is equal to 0.
So this one is the first derivative of y with respect to x is equal to 3x squared plus 4x plus 2 over 2 times y minus 1.
We have second derivative of y, plus 4 times the first derivative, plus 4y is equal to 0.
Linear equation, because you have the second derivative, the first derivative, and y, but they're not multiplied by the function or the derivatives. .
So hopefully you appreciate the usefulness of inflection points, and second derivative, and first derivative, in graphing some of these functions.
That's just g prime prime, plus h prime prime, plus B times-- the first derivative of this thing-- g prime plus h prime, plus C times-- this function-- g plus h.
Let's say I have the differential equation the second derivative of y minus 3 times the first derivative minus 4 times y is equal to 3e to the 2x.
So the second derivative of y with respect to x, plus 2 times the first derivative of y with respect to x, minus 3 y is equal to 0.