chain rule two composite functions ?

[bimbo36]

 

 

 

derivative (outer function ) (whole terms) * derivative (inner function)

 

?

 

 

 

 

 

 

 

 

[Cap'n Refsmmat]

Yes. If it helps, you can rewrite it this way:

 

[math](\sin (x^3))^4[/math]

[bimbo36]

i have sort of figured out chain rule for two composite functions .. and thank god it works ..

 

 

sin x xrise 4 xrise 3

 

so this is three composite functions ..

 

i cant get the answer the way i am working with ..

 

 

 

i wish i had more examples to work out, of functions including only "two composite functions"

 

i will deal with three , later ...

[bimbo36]

d/dx sin = cosx

 

d/dx cosx = - sin x

 

d/dx tanx = sec²x

 

 

 

 

then chain rule ...

 

composite two functions and composite three functions ...

 

 

 

d/dx f(x)og(x)

 

 

 

Df(x)og(x) * Dg(x)

 

------------------------------------------------------------------------------

 

 

d/dx f(x)og(x)oh(x)

 

Df(x)og(x)oh(x) * Dg(x)oh(x) *D h(x)

[Cap'n Refsmmat]

Looks like you're on the right track. Here's a simple example:

 

[math]\frac{d}{dx} ((x^5)^4)^3 = 3((x^5)^4)^2 \cdot \frac{d}{dx} (x^5)^4 = 3((x^5)^4)^2 \cdot 4 (x^5)^3 \cdot \frac{d}{dx} x^5[/math]