A derivative can be interpreted as the formula for slope of a secant line but it does not become a derivative until a limit is put in front of it. Derivatives can be used in many different ways. They are used for product rule, quotient rule, implicit, explicit, differentiation, chain rule, and for solving related rate problems.
Well guys, good luck on the test tomorrow. I'm doin this comment tonight cuz I'M LEAVIN FOR SHREVEPORT TOMORROW! WOO HOO!
Derivatives can be interpreted in a few different ways from what we have learned this year. Derivatives can be used in a variety of ways. There is the double derivative which jus means take the derivative of the derivative. There is the chain rule in which you follow the formula: ( derivative of outside ) ( recopy inside ) * ( derivative of inside ) Also there is the product rule which is done by using the formula ( copy the first ) ( derivative of the second ) + ( copy the second ) ( derivative of the first )
-Also you can do it by using the implicit derivative in which all you do extra is add a dy / dx every time you take the derivative of a " y " term .... then solve for dy / dx
There are many things that you need to find the derivative for some of them are: to find a derivative the long way and the short cut way, average velocity, the product rule and the quotient rule, how to find the equation of a tangent line, how to find the slope of a normal line, the chain rule, implicit derivative and explicit derivative, second derivative with implicit derivatives, and how to solve related rate problems. All of these things you need to know how to find the derivative. these are also all the things that we have learned so far that you have to find the derivative in these problems. Here’s some examples of how you take some of the derivatives:
Derivatives are used for many different things including differentiation, implicit, and pretains to different rules such as the chain rule, the product rule and the quotient rule.
Here is an example:
this is using the product rule and implicit differentiation
So far this year we learned many different ways a derivative can be interpreted. You can find a derivative the long way or use the short cut method, use the product rule and the quotient rule, the chain rule, implicit derivative and explicit derivative, second derivative with implicit derivatives, and how to solve related rate problems. Some ways a problem might be worded if you have to take the derivative may include: find the equation of a tangent line, how to find the slope, take the derivative, dy/dx...
Derivatives are used to find the slope of a tangent line, slope of a line, and anything else we used them for in Calculus so far this year.
A derivative can be interpreted as the formula for slope of a secant line but it does not become a derivative until a limit is put in front of it. Derivatives can be used in many different ways. They are used for product rule, quotient rule, implicit, explicit, differentiation, chain rule, and for solving related rate problems.
ReplyDeleteExamples:
1) Chain Rule:
3(4-9x)^4
= 12(4-9x) X (-9)
= -108(4-9x)^3
2) Relates Rates:
y = 4(x^2-5x)
1. dy/dt=?
x=3
dx/dt=2
2. y=4(x^2-5x)
3. dy/dt=4(2x-5)
4. dy/dt = 4(2(3)-5)
= 4(6-5)
= 4
3) Implicit Derivatives:
coty = x-y
-sinydy/dx = 1 - 1dy/dx
-sinydy/dx + 1dy/dx = 1
dy/dx = -1/siny+1
Well guys, good luck on the test tomorrow. I'm doin this comment tonight cuz I'M LEAVIN FOR SHREVEPORT TOMORROW! WOO HOO!
ReplyDeleteDerivatives can be interpreted in a few different ways from what we have learned this year. Derivatives can be used in a variety of ways. There is the double derivative which jus means take the derivative of the derivative. There is the chain rule in which you follow the formula: ( derivative of outside ) ( recopy inside ) * ( derivative of inside ) Also there is the product rule which is done by using the formula ( copy the first ) ( derivative of the second ) + ( copy the second ) ( derivative of the first )
-Also you can do it by using the implicit derivative in which all you do extra is add a dy / dx every time you take the derivative of a " y " term .... then solve for dy / dx
There are many things that you need to find the derivative for some of them are: to find a derivative the long way and the short cut way, average velocity, the product rule and the quotient rule, how to find the equation of a tangent line, how to find the slope of a normal line, the chain rule, implicit derivative and explicit derivative, second derivative with implicit derivatives, and how to solve related rate problems. All of these things you need to know how to find the derivative. these are also all the things that we have learned so far that you have to find the derivative in these problems.
ReplyDeleteHere’s some examples of how you take some of the derivatives:
Using implicit derivatives
coty = x-y
-sinydy/dx = 1 - 1dy/dx
-sinydy/dx + 1dy/dx = 1
dy/dx = -1/siny+1
using the chain rule
3(4-9x)^4
= 12(4-9x) X (-9)
= -108(4-9x)^3
Derivatives are used for many different things including differentiation, implicit, and pretains to different rules such as the chain
ReplyDeleterule, the product rule and the quotient rule.
Here is an example:
this is using the product rule and implicit
differentiation
xy=8
(x)(1dy/dx)+(y)(1)
xdy/dx+y
=-y/x
not too bad.
So far this year we learned many different ways a derivative can be interpreted. You can find a derivative the long way or use the short cut method, use the product rule and the quotient rule, the chain rule, implicit derivative and explicit derivative, second derivative with implicit derivatives, and how to solve related rate problems. Some ways a problem might be worded if you have to take the derivative may include: find the equation of a tangent line, how to find the slope, take the derivative, dy/dx...
ReplyDeleteDerivatives are used to find the slope of a tangent line, slope of a line, and anything else we used them for in Calculus so far this year.