No there is no order of operations when your looking for the chain rule. But you do have to set it up like this: the formula for the chain rule is: d/dx f(g(x) = f¹(g(x)) * g¹(x). the chain rule formula in word form: (take the derivative of the outside ( recopy the inside) * the derivative of the inside. When you are trying to find the outside and the inside you use y equals and u equals. Here are some examples how to set up you outside and inside: Outside inside Example: y =1/x+1 y = 1/u u = x+1 Example: y =sin (2x) y = sin u u = 2x Example: y = tan²x y = u² u= tan x (Tan x)² Here are some examples of how to do the chain rule: Example: d/dx (x²+1)³ y = u³ u = x²+1 3(x²+1)² * 2x =6x(x²+1)² Example: d/dx (3x-2x²)³ y = u³ u =3x-2x² 3(3x-2x²)³ * (3-4x) = 3(3-4x)(3x-2x²)²
No, there are no order of operations when working the chain rule. When doing the chain rule, the easiest way to think of it is: derivative of outside, recopy inside, multiply by derivative of inside. The "outside" y=f(u); the "inside" u= Example: g(x) = 3(4-9x)^4 y=2u^5 u=4-9x 12u^3(-9) 12(4-9x)^3 X -9 = -108(4-9x)^3 Example: y=cos^2x (cosx)^2 2(cosx) X 9(-sinx) 2cosxsinx = -sin2x
there is no specific operation that you follow when doing a problem that involves a chain rule. you first have to decide what is the outside and what is the inside.
this will start off the problem so be sure not to mix it up
after finding this you take the derivative of the outside, recopy the inside and multiply by the derivative of the inside.
No there is not an order of operations for the chain rule because of the way the formula and the rules for it work. The order that you would do the problem depends on what is on the inside and what is on the outside, there for the order of operations is not necessarily thrown out the window, but it is put to the side. Just follow the Chain Rule which states that you must: - Find the derivative of the of the outside, recopy the inside, multiply by the derivative of the inside. Here is an example: f (x) = 2 ( 2 – 9x )^3 y = 2u^3 u = 2 – 9x 6u^2 ( -9 ) 6 ( 2 – 9x )^3 * ( -9 ) -48 ( 2 – 9x )^3 **Note** As hard as it may be to believe, that is your final answer because it is in fully factored form, so DO NOT distribute the -48 or raise the equation 2 – 9x to the third power.
No there is no order of operations for the chain rule. The formula for the chain rule is: d / dx f ( g ( x ) = f'( g ( x ) ) times g'( x ). Or in word form: (take the derivative of the outside ( recopy the inside ) times the derivative of the inside. The outside of the problem is y and the inside of the problem is u... Ex. 3 ( x-2 )^2 y= 3 ( u )^2 u= x-2
Take the derivative of the outside and you should get this: 6 ( u )^1 Then recopy the inside: 6 ( x-2 )^1. Then you multiply by the derivative of the inside. In this case it would be 1 so you should get this...
When doing the chain rule their is no specific prder to do it in. The only thing that you have to realize is that do you do the chain rule before you do either the product or the quotient rule, or none of it. Everything is is more algabraic. Ex: (x^2)(x-2)^4 x^2 4(x-2)^3(1)+(x-2)^4 (2x) 4(x^2)(x-2)^3+2x(x-2)^4
No there is no order of operations when your looking for the chain rule. But you do have to set it up like this: the formula for the chain rule is: d/dx f(g(x) = f¹(g(x)) * g¹(x). the chain rule formula in word form: (take the derivative of the outside ( recopy the inside) * the derivative of the inside. When you are trying to find the outside and the inside you use y equals and u equals.
ReplyDeleteHere are some examples how to set up you outside and inside:
Outside inside
Example: y =1/x+1 y = 1/u u = x+1
Example: y =sin (2x) y = sin u u = 2x
Example: y = tan²x y = u² u= tan x
(Tan x)²
Here are some examples of how to do the chain rule:
Example: d/dx (x²+1)³ y = u³ u = x²+1
3(x²+1)² * 2x =6x(x²+1)²
Example: d/dx (3x-2x²)³ y = u³ u =3x-2x²
3(3x-2x²)³ * (3-4x) = 3(3-4x)(3x-2x²)²
No, there are no order of operations when working the chain rule. When doing the chain rule, the easiest way to think of it is: derivative of outside, recopy inside, multiply by derivative of inside. The "outside" y=f(u);
ReplyDeletethe "inside" u=
Example:
g(x) = 3(4-9x)^4
y=2u^5 u=4-9x
12u^3(-9)
12(4-9x)^3 X -9
= -108(4-9x)^3
Example:
y=cos^2x
(cosx)^2
2(cosx) X 9(-sinx)
2cosxsinx
= -sin2x
there is no specific operation
ReplyDeletethat you follow when doing a
problem that involves a chain rule.
you first have to decide what is
the outside and what is the inside.
this will start off the problem so
be sure not to mix it up
after finding this you take the derivative
of the outside, recopy the inside and multiply by the derivative of the inside.
here is an example:
d/dx (x^2+1)^3
3(x^2+1)x2x
=6x(x^2+1)^2
d/dx(3x-2x^2)^3
3(3x-2x^2)^2(3-4x)
No there is not an order of operations for the chain rule because of the way the formula and the rules for it work. The order that you would do the problem depends on what is on the inside and what is on the outside, there for the order of operations is not necessarily thrown out the window, but it is put to the side. Just follow the Chain Rule which states that you must:
ReplyDelete- Find the derivative of the of the outside, recopy the inside, multiply by the derivative of the inside.
Here is an example:
f (x) = 2 ( 2 – 9x )^3
y = 2u^3 u = 2 – 9x
6u^2 ( -9 )
6 ( 2 – 9x )^3 * ( -9 )
-48 ( 2 – 9x )^3
**Note** As hard as it may be to believe, that is your final answer because it is in fully factored form, so DO NOT distribute the -48 or raise the equation 2 – 9x to the third power.
No there is no order of operations for the chain rule. The formula for the chain rule is: d / dx f ( g ( x ) = f'( g ( x ) ) times g'( x ). Or in word form: (take the derivative of the outside ( recopy the inside ) times the derivative of the inside. The outside of the problem is y and the inside of the problem is u...
ReplyDeleteEx. 3 ( x-2 )^2
y= 3 ( u )^2 u= x-2
Take the derivative of the outside and you should get this: 6 ( u )^1 Then recopy the inside: 6 ( x-2 )^1. Then you multiply by the derivative of the inside. In this case it would be 1 so you should get this...
= 6 ( x-2 )( 1 )
Then you finish the problem and your answer is...
= 6 ( x-2 )
When doing the chain rule their is no specific prder to do it in. The only thing that you have to realize is that do you do the chain rule before you do either the product or the quotient rule, or none of it. Everything is is more algabraic.
ReplyDeleteEx: (x^2)(x-2)^4
x^2 4(x-2)^3(1)+(x-2)^4 (2x)
4(x^2)(x-2)^3+2x(x-2)^4